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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/Jacobsthal-numbers/00-META.yaml Normal file
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---
from: http://rosettacode.org/wiki/Jacobsthal_numbers

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'''Jacobsthal numbers''' are an integer sequence related to Fibonacci numbers. Similar to Fibonacci, where each term is the sum of the previous two terms, each term is the sum of the previous, plus twice the one before that. Traditionally the sequence starts with the given terms 0, 1.
<span style="font-size:125%;font-weight:bold;">
J<sub>0</sub> = 0
J<sub>1</sub> = 1
J<sub>n</sub> = J<sub>n-1</sub> + 2 × J<sub>n-2</sub>
</span>
Terms may be calculated directly using one of several possible formulas:
<span style="font-size:125%;font-weight:bold;">
J<sub>n</sub> = ( 2<sup>n</sup> - (-1)<sup>n</sup> ) / 3
</span>
'''Jacobsthal-Lucas numbers''' are very similar. They have the same recurrence relationship, the only difference is an initial starting value '''J<sub>0</sub> = 2''' rather than '''J<sub>0</sub> = 0'''.
Terms may be calculated directly using one of several possible formulas:
<span style="font-size:125%;font-weight:bold;">
JL<sub>n</sub> = 2<sup>n</sup> + (-1)<sup>n</sup>
</span>
'''Jacobsthal oblong numbers''' is the sequence obtained from multiplying each '''Jacobsthal number''' '''J<sub>n</sub>''' by its direct successor '''J<sub>n+1</sub>'''.
'''Jacobsthal primes''' are '''Jacobsthal numbers''' that are prime.
;Task
* Find and display the first 30 '''Jacobsthal numbers'''
* Find and display the first 30 '''Jacobsthal-Lucas numbers'''
* Find and display the first 20 '''Jacobsthal oblong numbers'''
* Find and display at least the first 10 '''Jacobsthal primes'''
;See also
;* [[wp:Jacobsthal_number|Wikipedia: Jacobsthal number]]
;* [https://www.numbersaplenty.com/set/Jacobsthal_number Numbers Aplenty - Jacobsthal number]
;* [[oeis:A001045|OEIS:A001045 - Jacobsthal sequence (or Jacobsthal numbers)]]
;* [[oeis:A014551|OEIS:A014551 - Jacobsthal-Lucas numbers.]]
;* [[oeis:A084175|OEIS:A084175 - Jacobsthal oblong numbers]]
;* [[oeis:A049883|OEIS:A049883 - Primes in the Jacobsthal sequence]]
;* [[Fibonacci sequence|Related task: Fibonacci sequence]]
;* [[Leonardo numbers|Related task: Leonardo numbers]]

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Task/Jacobsthal-numbers/11l/jacobsthal-numbers.11l Normal file
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F isPrime(n)
L(i) 2 .. Int(n ^ 0.5)
I n % i == 0
R 0B
R 1B
F odd(n)
R n [&] 1 != 0
F jacobsthal(n)
R floori((pow(2.0, n) + odd(n)) / 3)
F jacobsthal_lucas(n)
R Int(pow(2, n) + pow(-1, n))
F jacobsthal_oblong(n)
R Int64(jacobsthal(n)) * jacobsthal(n + 1)
print(‘First 30 Jacobsthal numbers:’)
L(j) 0..29
print(jacobsthal(j), end' ‘ ’)
print("\n\nFirst 30 Jacobsthal-Lucas numbers: ")
L(j) 0..29
print(jacobsthal_lucas(j), end' "\t")
print("\n\nFirst 20 Jacobsthal oblong numbers: ")
L(j) 0..19
print(jacobsthal_oblong(j), end' ‘ ’)
print("\n\nFirst 10 Jacobsthal primes: ")
L(j) 3..32
I isPrime(jacobsthal(j))
print(jacobsthal(j))

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Task/Jacobsthal-numbers/ALGOL-68/jacobsthal-numbers.alg Normal file
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BEGIN # find some Jacobsthal and related Numbers #
INT max jacobsthal = 29; # highest Jacobsthal number we will find #
INT max oblong = 20; # highest Jacobsthal oblong number we will find #
INT max j prime = 20; # number of Jacobsthal prinmes we will find #
PR precision 200 PR # set the precision of LONG LONG INT #
PR read "primes.incl.a68" PR # include prime utilities #
[ 0 : max jacobsthal ]LONG INT j; # will hold Jacobsthal numbers #
[ 0 : max jacobsthal ]LONG INT jl; # will hold Jacobsthal-Lucas numbers #
[ 1 : max oblong ]LONG INT jo; # will hold Jacobsthal oblong numbers #
# calculate the Jacobsthal Numbers and related numbers #
# Jacobsthal : J0 = 0, J1 = 1, Jn = Jn-1 + 2 × Jn-2 #
# Jacobsthal-Lucas: JL0 = 2, JL1 = 1, JLn = JLn-1 + 2 × JLn-2 #
# Jacobsthal oblong: JOn = Jn x Jn-1 #
j[ 0 ] := 0; j[ 1 ] := 1; jl[ 0 ] := 2; jl[ 1 ] := 1; jo[ 1 ] := 0;
FOR n FROM 2 TO UPB j DO
j[ n ] := j[ n - 1 ] + ( 2 * j[ n - 2 ] );
jl[ n ] := jl[ n - 1 ] + ( 2 * jl[ n - 2 ] )
OD;
FOR n TO UPB jo DO
jo[ n ] := j[ n ] * j[ n - 1 ]
OD;
# prints an array of numbers with the specified legend #
PROC show numbers = ( STRING legend, []LONG INT numbers )VOID:
BEGIN
INT n count := 0;
print( ( "First ", whole( ( UPB numbers - LWB numbers ) + 1, 0 ), " ", legend, newline ) );
FOR n FROM LWB numbers TO UPB numbers DO
print( ( " ", whole( numbers[ n ], -11 ) ) );
IF ( n count +:= 1 ) MOD 5 = 0 THEN print( ( newline ) ) FI
OD
END # show numbers # ;
# show the various numbers numbers #
show numbers( "Jacobsthal Numbers:", j );
show numbers( "Jacobsthal-Lucas Numbers:", jl );
show numbers( "Jacobsthal oblong Numbers:", jo );
# find some prime Jacobsthal numbers #
LONG LONG INT jn1 := j[ 1 ], jn2 := j[ 0 ];
INT p count := 0;
print( ( "First ", whole( max j prime, 0 ), " Jacobstal primes:", newline ) );
print( ( " n Jn", newline ) );
FOR n FROM 2 WHILE p count < max j prime DO
LONG LONG INT jn = jn1 + ( 2 * jn2 );
jn2 := jn1;
jn1 := jn;
IF is probably prime( jn ) THEN
# have a probably prime Jacobsthal number #
p count +:= 1;
print( ( whole( n, -4 ), ": ", whole( jn, 0 ), newline ) )
FI
OD
END

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Task/Jacobsthal-numbers/AppleScript/jacobsthal-numbers-1.applescript Normal file
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on jacobsthalNumbers(variant, n)
-- variant: text containing "Lucas", "oblong", or "prime" — or none of these.
-- n: length of output sequence required.
-- The two Jacobsthal numbers preceding the current 'j'. Initially the first two in the sequence.
set {anteprev, prev} to {0, 1}
-- Default plug-in script. Its handler simply appends the current 'j' to the output.
script o
property output : {anteprev, prev}
on append(dummy, j)
set end of output to j
end append
end script
-- If a variant sequence is specified, change the first value or substitute
-- a script whose handler decides the values to append to the output.
ignoring case
if (variant contains "Lucas") then
set anteprev to 2
set o's output's first item to anteprev
else if (variant contains "oblong") then
script
property output : {0}
on append(prev, j)
set end of output to prev * j
end append
end script
set o to result
else if (variant contains "prime") then
script
property output : {}
on append(dummy, j)
if (isPrime(j)) then set end of output to j
end append
end script
set o to result
end if
end ignoring
-- Work through the Jacobsthal process until the required output length is obtained.
repeat until ((count o's output) = n)
set j to anteprev + anteprev + prev
tell o to append(prev, j)
set anteprev to prev
set prev to j
end repeat
return o's output
end jacobsthalNumbers
on isPrime(n)
if (n < 3) then return (n is 2)
if (n mod 2 is 0) then return false
repeat with i from 3 to (n ^ 0.5) div 1 by 2
if (n mod i is 0) then return false
end repeat
return true
end isPrime
-- Task and presentation of results!:
on intToText(n)
set txt to ""
repeat until (n < 100000000)
set txt to text 2 thru 9 of (100000000 + (n mod 100000000) div 1 as text) & txt
set n to n div 100000000
end repeat
return (n as integer as text) & txt
end intToText
on chopList(theList, sublistLen)
script o
property lst : theList
property output : {}
end script
set listLen to (count o's lst)
repeat with i from 1 to listLen by sublistLen
set j to i + sublistLen - 1
if (j > listLen) then set j to listLen
set end of o's output to items i thru j of o's lst
end repeat
return o's output
end chopList
on matrixToText(matrix, w)
script o
property matrix : missing value
property row : missing value
end script
set o's matrix to matrix
set padding to " "
repeat with r from 1 to (count o's matrix)
set o's row to o's matrix's item r
repeat with i from 1 to (count o's row)
set o's row's item i to text -w thru end of (padding & o's row's item i)
end repeat
set o's matrix's item r to join(o's row, "")
end repeat
return join(o's matrix, linefeed)
end matrixToText
on join(lst, delim)
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to delim
set txt to lst as text
set AppleScript's text item delimiters to astid
return txt
end join
on task()
set output to {"First 30 Jacobsthal Numbers:", "First 30 Jacobsthal-Lucas Numbers:", ¬
"First 20 Jacobsthal oblong Numbers:", "First 11 Jacobsthal Primes:"}
set results to {jacobsthalNumbers("", 30), jacobsthalNumbers("Lucas", 30), ¬
jacobsthalNumbers("oblong", 20), jacobsthalNumbers("prime", 11)}
repeat with i from 1 to 4
set thisSequence to item i of results
repeat with j in thisSequence
set j's contents to intToText(j)
end repeat
if (i < 4) then
set theLines to chopList(thisSequence, 10)
else
set theLines to chopList(thisSequence, 6)
end if
set item i of output to item i of output & linefeed & matrixToText(theLines, (count end of thisSequence) + 1)
end repeat
return join(output, linefeed & linefeed)
end task
task()

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"First 30 Jacobsthal Numbers:
0 1 1 3 5 11 21 43 85 171
341 683 1365 2731 5461 10923 21845 43691 87381 174763
349525 699051 1398101 2796203 5592405 11184811 22369621 44739243 89478485 178956971
First 30 Jacobsthal-Lucas Numbers:
2 1 5 7 17 31 65 127 257 511
1025 2047 4097 8191 16385 32767 65537 131071 262145 524287
1048577 2097151 4194305 8388607 16777217 33554431 67108865 134217727 268435457 536870911
First 20 Jacobsthal oblong Numbers:
0 1 3 15 55 231 903 3655 14535 58311
232903 932295 3727815 14913991 59650503 238612935 954429895 3817763271 15270965703 61084037575
First 11 Jacobsthal Primes:
3 5 11 43 683 2731
43691 174763 2796203 715827883 2932031007403"

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-------------------- JACOBSTHAL NUMBERS ------------------
-- e.g. take(10, jacobsthal())
-- jacobsthal :: [Int]
on jacobsthal()
-- The terms of OEIS:A001045 as a non-finite sequence.
jacobsthalish(0, 1)
end jacobsthal
-- jacobsthal :: (Int, Int) -> [Int]
on jacobsthalish(x, y)
-- An infinite sequence of the terms of the
-- Jacobsthal-type series which begins with x and y.
script go
on |λ|(ab)
set {a, b} to ab
{a, {b, (2 * a) + b}}
end |λ|
end script
unfoldr(go, {x, y})
end jacobsthalish
-------------------------- TESTS -------------------------
on run
unlines(map(fShow, {¬
{"terms of the Jacobsthal sequence", ¬
30, jacobsthal()}, ¬
{"Jacobsthal-Lucas numbers", ¬
30, jacobsthalish(2, 1)}, ¬
{"Jacobsthal oblong numbers", ¬
20, zipWith(my mul, jacobsthal(), drop(1, jacobsthal()))}, ¬
{"primes in the Jacobsthal sequence", ¬
10, filter(isPrime, jacobsthal())}}))
end run
------------------------ FORMATTING ----------------------
on fShow(test)
set {k, n, xs} to test
str(n) & " first " & k & ":" & linefeed & ¬
table(5, map(my str, take(n, xs))) & linefeed
end fShow
-- justifyRight :: Int -> Char -> String -> String
on justifyRight(n, cFiller)
script go
on |λ|(s)
if n > length of s then
text -n thru -1 of ((replicate(n, cFiller) as text) & s)
else
s
end if
end |λ|
end script
end justifyRight
-- Egyptian multiplication - progressively doubling a list, appending
-- stages of doubling to an accumulator where needed for binary
-- assembly of a target length
-- replicate :: Int -> String -> String
on replicate(n, s)
-- Egyptian multiplication - progressively doubling a list,
-- appending stages of doubling to an accumulator where needed
-- for binary assembly of a target length
script p
on |λ|({n})
n ≤ 1
end |λ|
end script
script f
on |λ|({n, dbl, out})
if (n mod 2) > 0 then
set d to out & dbl
else
set d to out
end if
{n div 2, dbl & dbl, d}
end |λ|
end script
set xs to |until|(p, f, {n, s, ""})
item 2 of xs & item 3 of xs
end replicate
-- table :: Int -> [String] -> String
on table(n, xs)
-- A list of strings formatted as
-- right-justified rows of n columns.
set w to length of last item of xs
unlines(map(my unwords, ¬
chunksOf(n, map(justifyRight(w, space), xs))))
end table
-- unlines :: [String] -> String
on unlines(xs)
-- A single string formed by the intercalation
-- of a list of strings with the newline character.
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set s to xs as text
set my text item delimiters to dlm
s
end unlines
-- until :: (a -> Bool) -> (a -> a) -> a -> a
on |until|(p, f, x)
set v to x
set mp to mReturn(p)
set mf to mReturn(f)
repeat until mp's |λ|(v)
set v to mf's |λ|(v)
end repeat
v
end |until|
-- unwords :: [String] -> String
on unwords(xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, space}
set s to xs as text
set my text item delimiters to dlm
return s
end unwords
------------------------- GENERIC ------------------------
-- Just :: a -> Maybe a
on Just(x)
-- Constructor for an inhabited Maybe (option type) value.
-- Wrapper containing the result of a computation.
{type:"Maybe", Nothing:false, Just:x}
end Just
-- Nothing :: Maybe a
on Nothing()
-- Constructor for an empty Maybe (option type) value.
-- Empty wrapper returned where a computation is not possible.
{type:"Maybe", Nothing:true}
end Nothing
-- abs :: Num -> Num
on abs(x)
-- Absolute value.
if 0 > x then
-x
else
x
end if
end abs
-- any :: (a -> Bool) -> [a] -> Bool
on any(p, xs)
-- Applied to a predicate and a list,
-- |any| returns true if at least one element of the
-- list satisfies the predicate.
tell mReturn(p)
set lng to length of xs
repeat with i from 1 to lng
if |λ|(item i of xs) then return true
end repeat
false
end tell
end any
-- chunksOf :: Int -> [a] -> [[a]]
on chunksOf(k, xs)
script
on go(ys)
set ab to splitAt(k, ys)
set a to item 1 of ab
if {} ≠ a then
{a} & go(item 2 of ab)
else
a
end if
end go
end script
result's go(xs)
end chunksOf
-- drop :: Int -> [a] -> [a]
-- drop :: Int -> String -> String
on drop(n, xs)
take(n, xs) -- consumed
xs
end drop
-- enumFromThenTo :: Int -> Int -> Int -> [Int]
on enumFromThenTo(x1, x2, y)
set xs to {}
set gap to x2 - x1
set d to max(1, abs(gap)) * (signum(gap))
repeat with i from x1 to y by d
set end of xs to i
end repeat
return xs
end enumFromThenTo
-- filter :: (a -> Bool) -> Gen [a] -> Gen [a]
on filter(p, gen)
-- Non-finite stream of values which are
-- drawn from gen, and satisfy p
script
property mp : mReturn(p)'s |λ|
on |λ|()
set v to gen's |λ|()
repeat until mp(v)
set v to gen's |λ|()
end repeat
return v
end |λ|
end script
end filter
-- isPrime :: Int -> Bool
on isPrime(n)
-- True if n is prime
if {2, 3} contains n then return true
if 2 > n or 0 = (n mod 2) then return false
if 9 > n then return true
if 0 = (n mod 3) then return false
script p
on |λ|(x)
0 = n mod x or 0 = n mod (2 + x)
end |λ|
end script
not any(p, enumFromThenTo(5, 11, 1 + (n ^ 0.5)))
end isPrime
-- length :: [a] -> Int
on |length|(xs)
set c to class of xs
if list is c or string is c then
length of xs
else
(2 ^ 29 - 1) -- (maxInt - simple proxy for non-finite)
end if
end |length|
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
-- The list obtained by applying f
-- to each element of xs.
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- max :: Ord a => a -> a -> a
on max(x, y)
if x > y then
x
else
y
end if
end max
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
-- 2nd class handler function lifted into 1st class script wrapper.
if script is class of f then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- mul (*) :: Num a => a -> a -> a
on mul(a, b)
a * b
end mul
-- signum :: Num -> Num
on signum(x)
if x < 0 then
-1
else if x = 0 then
0
else
1
end if
end signum
-- splitAt :: Int -> [a] -> ([a], [a])
on splitAt(n, xs)
if n > 0 and n < length of xs then
if class of xs is text then
{items 1 thru n of xs as text, ¬
items (n + 1) thru -1 of xs as text}
else
{items 1 thru n of xs, items (n + 1) thru -1 of xs}
end if
else
if n < 1 then
{{}, xs}
else
{xs, {}}
end if
end if
end splitAt
-- str :: a -> String
on str(x)
x as string
end str
-- take :: Int -> [a] -> [a]
-- take :: Int -> String -> String
on take(n, xs)
set ys to {}
repeat with i from 1 to n
set v to |λ|() of xs
if missing value is v then
return ys
else
set end of ys to v
end if
end repeat
return ys
end take
-- uncons :: [a] -> Maybe (a, [a])
on uncons(xs)
set lng to |length|(xs)
if 0 = lng then
Nothing()
else
if (2 ^ 29 - 1) as integer > lng then
if class of xs is string then
set cs to text items of xs
Just({item 1 of cs, rest of cs})
else
Just({item 1 of xs, rest of xs})
end if
else
set nxt to take(1, xs)
if {} is nxt then
Nothing()
else
Just({item 1 of nxt, xs})
end if
end if
end if
end uncons
-- unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
on unfoldr(f, v)
-- A lazy (generator) list unfolded from a seed value
-- by repeated application of f to a value until no
-- residue remains. Dual to fold/reduce.
-- f returns either nothing (missing value)
-- or just (value, residue).
script
property valueResidue : {v, v}
property g : mReturn(f)
on |λ|()
set valueResidue to g's |λ|(item 2 of (valueResidue))
if missing value ≠ valueResidue then
item 1 of (valueResidue)
else
missing value
end if
end |λ|
end script
end unfoldr
-- zipWith :: (a -> b -> c) -> Gen [a] -> Gen [b] -> Gen [c]
on zipWith(f, ga, gb)
script
property ma : missing value
property mb : missing value
property mf : mReturn(f)
on |λ|()
if missing value is ma then
set ma to uncons(ga)
set mb to uncons(gb)
end if
if Nothing of ma or Nothing of mb then
missing value
else
set ta to Just of ma
set tb to Just of mb
set ma to uncons(item 2 of ta)
set mb to uncons(item 2 of tb)
|λ|(item 1 of ta, item 1 of tb) of mf
end if
end |λ|
end script
end zipWith

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Task/Jacobsthal-numbers/Arturo/jacobsthal-numbers.arturo Normal file
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J: function [n]-> ((2^n) - (neg 1)^n)/3
JL: function [n]-> (2^n) + (neg 1)^n
JO: function [n]-> (J n) * (J n+1)
printFirst: function [label, what, predicate, count][
print ["First" count label++":"]
result: new []
i: 0
while [count > size result][
num: do ~"|what| i"
if do predicate -> 'result ++ num
i: i + 1
]
(predicate=[true])? [
loop split.every: 5 result 'row [
print map to [:string] row 'item -> pad item 12
]
][
loop result 'row -> print row
]
print ""
]
printFirst "Jacobsthal numbers" 'J [true] 30
printFirst "Jacobsthal-Lucas numbers" 'JL [true] 30
printFirst "Jacobsthal oblong numbers" 'JO [true] 20
printFirst "Jacobsthal primes" 'J [prime? num] 20

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Task/Jacobsthal-numbers/AutoHotkey/jacobsthal-numbers-1.ahk Normal file
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Jacobsthal(n){
return SubStr(" " Format("{:.0f}", (2**n - (-1)**n ) / 3), -8)
}
Jacobsthal_Lucas(n){
return SubStr(" " Format("{:.0f}", 2**n + (-1)**n), -8)
}
prime_numbers(n) {
if (n <= 3)
return [n]
ans := [], done := false
while !done {
if !Mod(n,2)
ans.push(2), n /= 2
else if !Mod(n,3)
ans.push(3), n /= 3
else if (n = 1)
return ans
else {
sr := sqrt(n), done := true, i := 6
while (i <= sr+6) {
if !Mod(n, i-1) { ; is n divisible by i-1?
ans.push(i-1), n /= i-1, done := false
break
}
if !Mod(n, i+1) { ; is n divisible by i+1?
ans.push(i+1), n /= i+1, done := false
break
}
i += 6
}}}
ans.push(n)
return ans
}

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Task/Jacobsthal-numbers/AutoHotkey/jacobsthal-numbers-2.ahk Normal file
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result := "First 30 Jacobsthal numbers:`n"
loop 30
result .= Jacobsthal(A_Index-1) (mod(A_Index, 5) ? " ":"`n")
result .= "`nFirst 30 Jacobsthal-Lucas numbers:`n"
loop 30
result .= Jacobsthal_Lucas(A_Index-1) (mod(A_Index, 5) ? " ":"`n")
result .= "`nFirst 20 Jacobsthal oblong numbers:`n"
loop 20
result .= SubStr(" " Jacobsthal(A_Index-1) * Jacobsthal(A_Index), -8) (mod(A_Index, 5) ? " ":"`n")
result .= "`nFirst 10 Jacobsthal primes:`n"
c:=0
while c < 10
if (prime_numbers(x:=Jacobsthal(A_Index)).Count() = 1 && x > 1)
result .= x (mod(++c, 5) ? " ":"`n")
MsgBox, 262144, , % result
return

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#include <gmpxx.h>
#include <iomanip>
#include <iostream>
using big_int = mpz_class;
bool is_probably_prime(const big_int& n) {
return mpz_probab_prime_p(n.get_mpz_t(), 30) != 0;
}
big_int jacobsthal_number(unsigned int n) {
return ((big_int(1) << n) - (n % 2 == 0 ? 1 : -1)) / 3;
}
big_int jacobsthal_lucas_number(unsigned int n) {
return (big_int(1) << n) + (n % 2 == 0 ? 1 : -1);
}
big_int jacobsthal_oblong_number(unsigned int n) {
return jacobsthal_number(n) * jacobsthal_number(n + 1);
}
int main() {
std::cout << "First 30 Jacobsthal Numbers:\n";
for (unsigned int n = 0; n < 30; ++n) {
std::cout << std::setw(9) << jacobsthal_number(n)
<< ((n + 1) % 5 == 0 ? '\n' : ' ');
}
std::cout << "\nFirst 30 Jacobsthal-Lucas Numbers:\n";
for (unsigned int n = 0; n < 30; ++n) {
std::cout << std::setw(9) << jacobsthal_lucas_number(n)
<< ((n + 1) % 5 == 0 ? '\n' : ' ');
}
std::cout << "\nFirst 20 Jacobsthal oblong Numbers:\n";
for (unsigned int n = 0; n < 20; ++n) {
std::cout << std::setw(11) << jacobsthal_oblong_number(n)
<< ((n + 1) % 5 == 0 ? '\n' : ' ');
}
std::cout << "\nFirst 20 Jacobsthal primes:\n";
for (unsigned int n = 0, count = 0; count < 20; ++n) {
auto jn = jacobsthal_number(n);
if (is_probably_prime(jn)) {
++count;
std::cout << jn << '\n';
}
}
}

61
Task/Jacobsthal-numbers/C/jacobsthal-numbers.c Normal file
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#include <stdio.h>
#include <gmp.h>
void jacobsthal(mpz_t r, unsigned long n) {
mpz_t s;
mpz_init(s);
mpz_set_ui(r, 1);
mpz_mul_2exp(r, r, n);
mpz_set_ui(s, 1);
if (n % 2) mpz_neg(s, s);
mpz_sub(r, r, s);
mpz_div_ui(r, r, 3);
}
void jacobsthal_lucas(mpz_t r, unsigned long n) {
mpz_t a;
mpz_init(a);
mpz_set_ui(r, 1);
mpz_mul_2exp(r, r, n);
mpz_set_ui(a, 1);
if (n % 2) mpz_neg(a, a);
mpz_add(r, r, a);
}
int main() {
int i, count;
mpz_t jac[30], j;
printf("First 30 Jacobsthal numbers:\n");
for (i = 0; i < 30; ++i) {
mpz_init(jac[i]);
jacobsthal(jac[i], i);
gmp_printf("%9Zd ", jac[i]);
if (!((i+1)%5)) printf("\n");
}
printf("\nFirst 30 Jacobsthal-Lucas numbers:\n");
mpz_init(j);
for (i = 0; i < 30; ++i) {
jacobsthal_lucas(j, i);
gmp_printf("%9Zd ", j);
if (!((i+1)%5)) printf("\n");
}
printf("\nFirst 20 Jacobsthal oblong numbers:\n");
for (i = 0; i < 20; ++i) {
mpz_mul(j, jac[i], jac[i+1]);
gmp_printf("%11Zd ", j);
if (!((i+1)%5)) printf("\n");
}
printf("\nFirst 20 Jacobsthal primes:\n");
for (i = 0, count = 0; count < 20; ++i) {
jacobsthal(j, i);
if (mpz_probab_prime_p(j, 15) > 0) {
gmp_printf("%Zd\n", j);
++count;
}
}
return 0;
}

91
Task/Jacobsthal-numbers/Delphi/jacobsthal-numbers.delphi Normal file
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procedure GetJacobsthalNum(Lucas: boolean; Max: integer; var IA: TInt64DynArray);
{Get Jacobsthal number sequence. If Lucas is true do Lucal variation}
var I: integer;
begin
SetLength(IA,Max);
{Lucas starts sequence with 2 instead of 0}
if Lucas then IA[0]:=2 else IA[0]:=0;
IA[1]:=1;
{Calculate Nn = Nn-1 + 2 Nn-2}
for I:=2 to Max-1 do
IA[I]:=IA[I-1] + 2 * IA[I-2];
end;
procedure GetJacobsthalOblong(Max: integer; var IA: TInt64DynArray);
{Jacobsthal Oblong numbers is Nn = Jn x Jn=1 where J = Jacobsthal numbers}
var IA2: TInt64DynArray;
var I: integer;
begin
GetJacobsthalNum(False,Max+1,IA2);
SetLength(IA,Max);
for I:=0 to High(IA2)-1 do
begin
IA[I]:=IA2[I] * IA2[I+1];
end;
end;
procedure GetJacobsthalPrimes(Memo: TMemo);
var I: integer;
var Jacob,N1, N2: int64;
function GetNext: int64;
{Nn = Nn-1 + 2 x Nn-2}
begin
Result:=N1 + 2 * N2;
N2:=N1; N1:=Result;
end;
begin
N2:=0; N1:=1;
for I:=1 to 10 do
begin
repeat Jacob:=GetNext;
until IsPrime(Jacob);
Memo.Lines.Add(IntToStr(I)+' - '+IntToStr(Jacob));
end;
end;
procedure ShowJacobsthalNumbers(Memo: TMemo);
var I: integer;
var IA: TInt64DynArray;
var S: string;
begin
GetJacobsthalNum(False,30,IA);
Memo.Lines.Add('First 30 Jacobsthal Numbers');
S:='';
for I:=0 to High(IA) do
begin
S:=S+Format('%12.0n',[IA[I]+0.0]);
if (I mod 5)=4 then S:=S+CRLF;
end;
Memo.Lines.Add(S);
Memo.Lines.Add('');
GetJacobsthalNum(True,30,IA);
Memo.Lines.Add('First 30 Jacobsthal-Lucas Numbers');
S:='';
for I:=0 to High(IA) do
begin
S:=S+Format('%14.0n',[IA[I]+0.0]);
if (I mod 4)=3 then S:=S+CRLF;
end;
Memo.Lines.Add(S);
Memo.Lines.Add('');
GetJacobsthalOblong(20,IA);
Memo.Lines.Add('First 20 Jacobsthal-Oblong Numbers');
S:='';
for I:=0 to High(IA) do
begin
S:=S+Format('%18.0n',[IA[I]+0.0]);
if (I mod 3)=2 then S:=S+CRLF;
end;
Memo.Lines.Add(S);
Memo.Lines.Add('');
GetJacobsthalPrimes(Memo);
end;

7
Task/Jacobsthal-numbers/F-Sharp/jacobsthal-numbers.fs Normal file
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// Jacobsthal numbers: Nigel Galloway January 10th., 2023
let J,JL=let fN g ()=Seq.unfold(fun(n,g)->Some(n,(g,g+2UL*n)))(g,1UL) in (fN 0UL,fN 2UL)
printf "First 30 Jacobsthal are "; J()|>Seq.take 30|>Seq.iter(printf "%d "); printfn ""
printf "First 30 Jacobsthal-Lucas are "; JL()|>Seq.take 30|>Seq.iter(printf "%d "); printfn ""
printf "First 20 Jacobsthal Oblong are "; J()|>Seq.pairwise|>Seq.take 20|>Seq.iter(fun(n,g)->printf "%d " (n*g)); printfn ""
let fN g= Open.Numeric.Primes.MillerRabin.IsPrime &g
printf "First 10 Jacobsthal Primes are "; J()|>Seq.filter fN|>Seq.take 10|>Seq.iter(printf "%d "); printfn ""

26
Task/Jacobsthal-numbers/Factor/jacobsthal-numbers.factor Normal file
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USING: grouping io kernel lists lists.lazy math math.functions
math.primes prettyprint sequences ;
: 2^-1^ ( n -- 2^n -1^n ) dup 2^ -1 rot ^ ;
: jacobsthal ( m -- n ) 2^-1^ - 3 / ;
: jacobsthal-lucas ( m -- n ) 2^-1^ + ;
: as-list ( quot -- list ) 0 lfrom swap lmap-lazy ; inline
: jacobsthals ( -- list ) [ jacobsthal ] as-list ;
: lucas-jacobthals ( -- list ) [ jacobsthal-lucas ] as-list ;
: prime-jacobsthals ( -- list ) jacobsthals [ prime? ] lfilter ;
: show ( n list -- ) ltake list>array 5 group simple-table. nl ;
: oblong ( -- list )
jacobsthals dup cdr lzip [ product ] lmap-lazy ;
"First 30 Jacobsthal numbers:" print
30 jacobsthals show
"First 30 Jacobsthal-Lucas numbers:" print
30 lucas-jacobthals show
"First 20 Jacobsthal oblong numbers:" print
20 oblong show
"First 20 Jacobsthal primes:" print
20 prime-jacobsthals ltake [ . ] leach

51
Task/Jacobsthal-numbers/FreeBASIC/jacobsthal-numbers.basic Normal file
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Function isPrime(n As Ulongint) As Boolean
If n < 2 Then Return False
If n Mod 2 = 0 Then Return false
For i As Uinteger = 3 To Int(Sqr(n))+1 Step 2
If n Mod i = 0 Then Return false
Next i
Return true
End Function
Dim Shared As Uinteger n(1)
Dim Shared As Uinteger i0 = 0, i1 = 1
Dim Shared As Integer j, c, P = 1, Q = -2
Print "First 30 Jacobsthal numbers:"
c = 0 : n(i0) = 0: n(i1) = 1
For j = 0 To 29
c += 1
Print Using " #########"; n(i0);
Print Iif (c Mod 5, "", !"\n");
n(i0) = P * n(i1) - Q * n(i0)
Swap i0, i1
Next j
Print !"\n\nFirst 30 Jacobsthal-Lucas numbers: "
c = 0 : n(i0) = 2: n(i1) = 1
For j = 0 To 29
c += 1
Print Using " #########"; n(i0);
Print Iif (c Mod 5, "", !"\n");
n(i0) = P * n(i1) - Q * n(i0)
Swap i0, i1
Next j
Print !"\n\nFirst 20 Jacobsthal oblong numbers: "
c = 0 : n(i0) = 0: n(i1) = 1
For j = 0 To 19
c += 1
Print Using " ###########"; n(i0)*n(i1);
Print Iif (c Mod 5, "", !"\n");
n(i0) = P * n(i1) - Q * n(i0)
Swap i0, i1
Next j
Print !"\n\nFirst 10 Jacobsthal primes: "
c = 0 : n(i0) = 0: n(i1) = 1
Do
If isPrime(n(i0)) Then c += 1 : Print n(i0)
n(i0) = P * n(i1) - Q * n(i0)
Swap i0, i1
Loop Until c = 10
Sleep

82
Task/Jacobsthal-numbers/Gambas/jacobsthal-numbers.gambas Normal file
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Public n As New Long[2]
Public Sub Main()
Dim i0 As Integer = 0, i1 As Integer = 1
Dim j As Integer, c As Integer, P As Integer = 1, Q As Integer = -2
Print "First 30 Jacobsthal numbers:"
c = 0
n[i0] = 0
n[i1] = 1
For j = 0 To 29
c += 1
Print Format$(n[i0], " #########");
If (c Mod 5) Then
Print "";
Else
Print Chr(10);
End If
n[i0] = P * n[i1] - Q * n[i0]
Swap i0, i1
Next
Print "\n\nFirst 30 Jacobsthal-Lucas numbers: "
c = 0
n[i0] = 2
n[i1] = 1
For j = 0 To 29
c += 1
Print Format$(n[i0], " #########");
If (c Mod 5) Then
Print "";
Else
Print Chr(10);
End If
n[i0] = P * n[i1] - Q * n[i0]
Swap i0, i1
Next
Print "\n\nFirst 20 Jacobsthal oblong numbers: "
c = 0
n[i0] = 0
n[i1] = 1
For j = 0 To 19
c += 1
Print Format$(n[i0] * n[i1], " ###########");
If (c Mod 5) Then
Print "";
Else
Print Chr(10);
End If
n[i0] = P * n[i1] - Q * n[i0]
Swap i0, i1
Next
Print "\n\nFirst 10 Jacobsthal primes: "
c = 0
n[i0] = 0
n[i1] = 1
Do
If isPrime(n[i0]) Then
c += 1
Print n[i0]
End If
n[i0] = P * n[i1] - Q * n[i0]
Swap i0, i1
Loop Until c = 10
End
Public Sub isPrime(ValorEval As Long) As Boolean
If ValorEval < 2 Then Return False
If ValorEval Mod 2 = 0 Then Return ValorEval = 2
If ValorEval Mod 3 = 0 Then Return ValorEval = 3
Dim d As Long = 5
While d * d <= ValorEval
If ValorEval Mod d = 0 Then Return False Else d += 2
Wend
Return True
End Function

65
Task/Jacobsthal-numbers/Go/jacobsthal-numbers.go Normal file
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package main
import (
"fmt"
"math/big"
)
func jacobsthal(n uint) *big.Int {
t := big.NewInt(1)
t.Lsh(t, n)
s := big.NewInt(1)
if n%2 != 0 {
s.Neg(s)
}
t.Sub(t, s)
return t.Div(t, big.NewInt(3))
}
func jacobsthalLucas(n uint) *big.Int {
t := big.NewInt(1)
t.Lsh(t, n)
a := big.NewInt(1)
if n%2 != 0 {
a.Neg(a)
}
return t.Add(t, a)
}
func main() {
jac := make([]*big.Int, 30)
fmt.Println("First 30 Jacobsthal numbers:")
for i := uint(0); i < 30; i++ {
jac[i] = jacobsthal(i)
fmt.Printf("%9d ", jac[i])
if (i+1)%5 == 0 {
fmt.Println()
}
}
fmt.Println("\nFirst 30 Jacobsthal-Lucas numbers:")
for i := uint(0); i < 30; i++ {
fmt.Printf("%9d ", jacobsthalLucas(i))
if (i+1)%5 == 0 {
fmt.Println()
}
}
fmt.Println("\nFirst 20 Jacobsthal oblong numbers:")
for i := uint(0); i < 20; i++ {
t := big.NewInt(0)
fmt.Printf("%11d ", t.Mul(jac[i], jac[i+1]))
if (i+1)%5 == 0 {
fmt.Println()
}
}
fmt.Println("\nFirst 20 Jacobsthal primes:")
for n, count := uint(0), 0; count < 20; n++ {
j := jacobsthal(n)
if j.ProbablyPrime(10) {
fmt.Println(j)
count++
}
}
}

25
Task/Jacobsthal-numbers/Haskell/jacobsthal-numbers-1.hs Normal file
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jacobsthal :: [Integer]
jacobsthal = 0 : 1 : zipWith (\x y -> 2 * x + y) jacobsthal (tail jacobsthal)
jacobsthalLucas :: [Integer]
jacobsthalLucas = 2 : 1 : zipWith (\x y -> 2 * x + y) jacobsthalLucas (tail jacobsthalLucas)
jacobsthalOblong :: [Integer]
jacobsthalOblong = zipWith (*) jacobsthal (tail jacobsthal)
isPrime :: Integer -> Bool
isPrime n = n > 1 && not (or [n `mod` i == 0 | i <- [2 .. floor (sqrt (fromInteger n))]])
main :: IO ()
main = do
putStrLn "First 30 Jacobsthal numbers:"
print $ take 30 jacobsthal
putStrLn ""
putStrLn "First 30 Jacobsthal-Lucas numbers:"
print $ take 30 jacobsthalLucas
putStrLn ""
putStrLn "First 20 Jacobsthal oblong numbers:"
print $ take 20 jacobsthalOblong
putStrLn ""
putStrLn "First 10 Jacobsthal primes:"
print $ take 10 $ filter isPrime jacobsthal

50
Task/Jacobsthal-numbers/Haskell/jacobsthal-numbers-2.hs Normal file
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import Data.List (intercalate, transpose, uncons, unfoldr)
import Data.List.Split (chunksOf)
import Data.Numbers.Primes (isPrime)
import Text.Printf (printf)
-------------------- JACOBSTHAL NUMBERS ------------------
jacobsthal :: [Integer]
jacobsthal = jacobsthalish (0, 1)
jacobsthalish :: (Integer, Integer) -> [Integer]
jacobsthalish = unfoldr go
where
go (a, b) = Just (a, (b, 2 * a + b))
--------------------------- TEST -------------------------
main :: IO ()
main =
mapM_
(putStrLn . format)
[ ( "terms of the Jacobsthal sequence",
30,
jacobsthal
),
( "Jacobsthal-Lucas numbers",
30,
jacobsthalish (2, 1)
),
( "Jacobsthal oblong numbers",
20,
zipWith (*) jacobsthal (tail jacobsthal)
),
( "Jacobsthal primes",
10,
filter isPrime jacobsthal
)
]
format :: (String, Int, [Integer]) -> String
format (k, n, xs) =
show n <> (' ' : k) <> ":\n"
<> table
" "
(chunksOf 5 $ show <$> take n xs)
table :: String -> [[String]] -> String
table gap rows =
let ws = maximum . fmap length <$> transpose rows
pw = printf . flip intercalate ["%", "s"] . show
in unlines $ intercalate gap . zipWith pw ws <$> rows

2
Task/Jacobsthal-numbers/J/jacobsthal-numbers-1.j Normal file
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ja=: 3 %~ 2x&^ - _1x&^ NB. Jacobsthal
jl=: 2x&^ + _1x&^ NB.Jacobsthal-Lucas

13
Task/Jacobsthal-numbers/J/jacobsthal-numbers-2.j Normal file
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ja i.3 10
0 1 1 3 5 11 21 43 85 171
341 683 1365 2731 5461 10923 21845 43691 87381 174763
349525 699051 1398101 2796203 5592405 11184811 22369621 44739243 89478485 178956971
jl i.3 10
2 1 5 7 17 31 65 127 257 511
1025 2047 4097 8191 16385 32767 65537 131071 262145 524287
1048577 2097151 4194305 8388607 16777217 33554431 67108865 134217727 268435457 536870911
2 10$2 */\ ja i.21 NB. Jacobsthal oblong
0 1 3 15 55 231 903 3655 14535 58311
232903 932295 3727815 14913991 59650503 238612935 954429895 3817763271 15270965703 61084037575
ja I.1 p:ja i.32 NB. first ten Jacobsthal primes
3 5 11 43 683 2731 43691 174763 2796203 715827883

72
Task/Jacobsthal-numbers/Java/jacobsthal-numbers.java Normal file
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import java.math.BigInteger;
public final class JacobsthalNumbers {
public static void main(String[] aArgs) {
System.out.println("The first 30 Jacobsthal Numbers:");
for ( int i = 0; i < 6; i++ ) {
for ( int k = 0; k < 5; k++ ) {
System.out.print(String.format("%15s", jacobsthalNumber(i * 5 + k)));
}
System.out.println();
}
System.out.println();
System.out.println("The first 30 Jacobsthal-Lucas Numbers:");
for ( int i = 0; i < 6; i++ ) {
for ( int k = 0; k < 5; k++ ) {
System.out.print(String.format("%15s", jacobsthalLucasNumber(i * 5 + k)));
}
System.out.println();
}
System.out.println();
System.out.println("The first 20 Jacobsthal oblong Numbers:");
for ( int i = 0; i < 4; i++ ) {
for ( int k = 0; k < 5; k++ ) {
System.out.print(String.format("%15s", jacobsthalOblongNumber(i * 5 + k)));
}
System.out.println();
}
System.out.println();
System.out.println("The first 10 Jacobsthal Primes:");
for ( int i = 0; i < 10; i++ ) {
System.out.println(jacobsthalPrimeNumber(i));
}
}
private static BigInteger jacobsthalNumber(int aIndex) {
BigInteger value = BigInteger.valueOf(parityValue(aIndex));
return BigInteger.ONE.shiftLeft(aIndex).subtract(value).divide(THREE);
}
private static long jacobsthalLucasNumber(int aIndex) {
return ( 1 << aIndex ) + parityValue(aIndex);
}
private static long jacobsthalOblongNumber(int aIndex) {
long nextJacobsthal = jacobsthalNumber(aIndex + 1).longValueExact();
long result = currentJacobsthal * nextJacobsthal;
currentJacobsthal = nextJacobsthal;
return result;
}
private static long jacobsthalPrimeNumber(int aIndex) {
BigInteger candidate = jacobsthalNumber(latestIndex++);
while ( ! candidate.isProbablePrime(CERTAINTY) ) {
candidate = jacobsthalNumber(latestIndex++);
}
return candidate.longValueExact();
}
private static int parityValue(int aIndex) {
return ( aIndex & 1 ) == 0 ? +1 : -1;
}
private static long currentJacobsthal = 0;
private static int latestIndex = 0;
private static final BigInteger THREE = BigInteger.valueOf(3);
private static final int CERTAINTY = 20;
}

17
Task/Jacobsthal-numbers/Jq/jacobsthal-numbers-1.jq Normal file
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# Split the input array into a stream of arrays
def chunks(n):
def c: .[0:n], (if length > n then .[n:]|c else empty end);
c;
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
# If $j is 0, then an error condition is raised;
# otherwise, assuming infinite-precision integer arithmetic,
# if the input and $j are integers, then the result will be a pair of integers.
def divmod($j):
. as $i
| ($i % $j) as $mod
| [($i - $mod) / $j, $mod] ;
# To take advantage of gojq's arbitrary-precision integer arithmetic:
def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);

26
Task/Jacobsthal-numbers/Jq/jacobsthal-numbers-2.jq Normal file
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def jacobsthal:
. as $n
| ( (2|power($n)) - (if ($n%2 == 0) then 1 else -1 end)) | divmod(3)[0];
def jacobsthalLucas:
. as $n
| (2|power($n)) + (if ($n%2 == 0) then 1 else -1 end);
def tasks:
def pp($width): chunks(5) | map(lpad($width)) | join("");
[range(0;30) | jacobsthal] as $js
| "First 30 Jacobsthal numbers:",
( $js | pp(12)),
"\nFirst 30 Jacobsthal-Lucas numbers:",
( [range(0;30) | jacobsthalLucas] | pp(12)),
"\nFirst 20 Jacobsthal oblong numbers:",
( [range(0;20) | $js[.] * $js[1+.]] | pp(14)),
"\nFirst 11 Jacobsthal primes:",
limit(11; range(0; infinite) | jacobsthal | select(is_prime))
;
tasks

23
Task/Jacobsthal-numbers/Julia/jacobsthal-numbers.julia Normal file
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using Lazy
using Primes
J(n) = (2^n - (-1)^n) ÷ 3
L(n) = 2^n + (-1)^n
Jacobsthal = @>> Lazy.range(0) map(J)
JLucas = @>> Lazy.range(0) map(L)
Joblong = @>> Lazy.range(big"0") map(n -> J(n) * J(n + 1))
Jprimes = @>> Lazy.range(big"0") map(J) filter(isprime)
function printrows(title, vec, columnsize = 15, columns = 5, rjust=true)
println(title)
for (i, n) in enumerate(vec)
print((rjust ? lpad : rpad)(n, columnsize), i % columns == 0 ? "\n" : "")
end
println()
end
printrows("Thirty Jacobsthal numbers:", collect(take(30, Jacobsthal)))
printrows("Thirty Jacobsthal-Lucas numbers:", collect(take(30, JLucas)))
printrows("Twenty oblong Jacobsthal numbers:", collect(take(20, Joblong)))
printrows("Fifteen Jacabsthal prime numbers:", collect(take(15, Jprimes)), 40, 1, false)

18
Task/Jacobsthal-numbers/Mathematica/jacobsthal-numbers.math Normal file
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ClearAll[Jacobsthal, JacobsthalLucas, JacobsthalOblong]
Jacobsthal[n_]:=(2^n-(-1)^n)/3
JacobsthalLucas[n_]:=2^n+(-1)^n
JacobsthalOblong[n_]:=Jacobsthal[n]Jacobsthal[n+1]
Jacobsthal[Range[0, 29]]
JacobsthalLucas[Range[0, 29]]
JacobsthalOblong[Range[0, 19]]
n=0;
i=0;
Reap[While[n<20,
If[
PrimeQ[Jacobsthal[i]]
,
Sow[{i,Jacobsthal[i]}];
n++;
];
i++;
]][[2,1]]//Grid

73
Task/Jacobsthal-numbers/Nim/jacobsthal-numbers.nim Normal file
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import std/strutils
func isPrime(n: Natural): bool =
## Return true if "n" is prime.
if n < 2: return false
if n mod 2 == 0: return n == 2
if n mod 3 == 0: return n == 3
var step = 2
var d = 5
while d * d <= n:
if n mod d == 0: return false
inc d, step
step = 6 - step
result = true
iterator jacobsthalSequence(first, second: int): int =
## Yield the successive Jacobsthal numbers or
## Jacobsthal-Lucas numbers.
var prev = first
var curr = second
yield prev
yield curr
while true:
swap prev, curr
curr += curr + prev
yield curr
iterator jacobsthalOblong(): int =
## Yield the successive Jacobsthal oblong numbers.
var prev = -1
for n in jacobsthalSequence(0, 1):
if prev >= 0:
yield prev * n
prev = n
iterator jacobsthalPrimes(): int =
## Yield the successive Jacobsthal prime numbers.
for n in jacobsthalSequence(0, 1):
if n.isPrime:
yield n
echo "First 30 Jacobsthal numbers:"
var count = 0
for n in jacobsthalSequence(0, 1):
inc count
stdout.write align($n, 11)
if count mod 6 == 0: echo()
if count == 30: break
echo "\nFirst 30 Jacobsthal-Lucas numbers:"
count = 0
for n in jacobsthalSequence(2, 1):
inc count
stdout.write align($n, 11)
if count mod 6 == 0: echo()
if count == 30: break
echo "\nFirst 20 Jacobsthal oblong numbers:"
count = 0
for n in jacobsthalOblong():
inc count
stdout.write align($n, 13)
if count mod 5 == 0: echo()
if count == 20: break
echo "\nFirst 10 Jacobsthal prime numbers:"
count = 0
for n in jacobsthalPrimes():
inc count
stdout.write align($n, 11)
if count mod 5 == 0: echo()
if count == 10: break

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let is_prime n =
let rec test x =
x * x > n || n mod x <> 0 && n mod (x + 2) <> 0 && test (x + 6)
in
if n < 5
then n land 2 <> 0
else n land 1 <> 0 && n mod 3 <> 0 && test 5
let seq_jacobsthal =
let rec next b a () = Seq.Cons (a, next (a + a + b) b) in
next 1
let seq_jacobsthal_oblong =
let rec next b a () = Seq.Cons (a * b, next (a + a + b) b) in
next 1 0
let () =
let show (n, seq, s) =
Seq.take n seq
|> Seq.fold_left (Printf.sprintf "%s %u") (Printf.sprintf "First %u %s numbers:\n" n s)
|> print_endline
in
List.iter show [
30, seq_jacobsthal 0, "Jacobsthal";
30, seq_jacobsthal 2, "Jacobsthal-Lucas";
20, seq_jacobsthal_oblong, "Jacobsthal oblong";
10, Seq.filter is_prime (seq_jacobsthal 0), "Jacobsthal prime"]

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Task/Jacobsthal-numbers/Perl/jacobsthal-numbers.pl Normal file
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use strict;
use warnings;
use feature <say state>;
use bigint;
use List::Util 'max';
use ntheory 'is_prime';
sub table { my $t = 5 * (my $c = 1 + length max @_); ( sprintf( ('%'.$c.'d')x@_, @_) ) =~ s/.{1,$t}\K/\n/gr }
sub jacobsthal { my($n) = @_; state @J = (0, 1); do { push @J, $J[-1] + 2 * $J[-2]} until @J > $n; $J[$n] }
sub jacobsthal_lucas { my($n) = @_; state @JL = (2, 1); do { push @JL, $JL[-1] + 2 * $JL[-2]} until @JL > $n; $JL[$n] }
my(@j,@jp,$c,$n);
push @j, jacobsthal $_ for 0..29;
do { is_prime($n = ( 2**++$c - -1**$c ) / 3) and push @jp, $n } until @jp == 20;
say "First 30 Jacobsthal numbers:\n", table @j;
say "First 30 Jacobsthal-Lucas numbers:\n", table map { jacobsthal_lucas $_-1 } 1..30;
say "First 20 Jacobsthal oblong numbers:\n", table map { $j[$_-1] * $j[$_] } 1..20;
say "First 20 Jacobsthal primes:\n", join "\n", @jp;

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Task/Jacobsthal-numbers/Phix/jacobsthal-numbers.phix Normal file
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(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">jacobsthal</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">((</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)+</span><span style="color: #7060A8;">odd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))/</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">jacobsthal_lucas</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)+</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">jacobsthal_oblong</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">jacobsthal</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">jacobsthal</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">jba</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">=</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">,{{</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">},</span><span style="color: #000000;">s</span><span style="color: #0000FF;">}),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">)}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"First 30 Jacobsthal numbers:\n%s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">jba</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%9d"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">29</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">),</span><span style="color: #000000;">jacobsthal</span><span style="color: #0000FF;">)))</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"First 30 Jacobsthal-Lucas numbers:\n%s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">jba</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%9d"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">29</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">),</span><span style="color: #000000;">jacobsthal_lucas</span><span style="color: #0000FF;">)))</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"First 20 Jacobsthal oblong numbers:\n%s\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">jba</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%11d"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">19</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">),</span><span style="color: #000000;">jacobsthal_oblong</span><span style="color: #0000FF;">)))</span>
<span style="color: #000080;font-style:italic;">--printf(1,"First 10 Jacobsthal primes:\n%s\n", jba("%d",filter(apply(tagset(31,0),jacobsthal),is_prime),1))
--hmm(""), fine, but to go further roll out gmp:</span>
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #004080;">mpz</span> <span style="color: #000000;">z</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">found</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"First 20 jacobsthal primes:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">found</span><span style="color: #0000FF;"><</span><span style="color: #000000;">20</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_add_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">odd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))</span>
<span style="color: #0000FF;">{}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_fdiv_q_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">found</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<!--

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Task/Jacobsthal-numbers/Python/jacobsthal-numbers-1.py Normal file
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#!/usr/bin/python
from math import floor, pow
def isPrime(n):
for i in range(2, int(n**0.5) + 1):
if n % i == 0:
return False
return True
def odd(n):
return n and 1 != 0
def jacobsthal(n):
return floor((pow(2,n)+odd(n))/3)
def jacobsthal_lucas(n):
return int(pow(2,n)+pow(-1,n))
def jacobsthal_oblong(n):
return jacobsthal(n)*jacobsthal(n+1)
if __name__ == '__main__':
print("First 30 Jacobsthal numbers:")
for j in range(0, 30):
print(jacobsthal(j), end=" ")
print("\n\nFirst 30 Jacobsthal-Lucas numbers: ")
for j in range(0, 30):
print(jacobsthal_lucas(j), end = '\t')
print("\n\nFirst 20 Jacobsthal oblong numbers: ")
for j in range(0, 20):
print(jacobsthal_oblong(j), end=" ")
print("\n\nFirst 10 Jacobsthal primes: ")
for j in range(3, 33):
if isPrime(jacobsthal(j)):
print(jacobsthal(j))

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'''Jacobsthal numbers'''
from itertools import islice
from operator import mul
# jacobsthal :: [Integer]
def jacobsthal():
'''Infinite sequence of terms of OEIS A001045
'''
return jacobsthalish(0, 1)
# jacobsthalish :: (Int, Int) -> [Int]
def jacobsthalish(*xy):
'''Infinite sequence of jacobsthal-type series
beginning with a, b
'''
def go(ab):
a, b = ab
return a, (b, 2 * a + b)
return unfoldr(go)(xy)
# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''First 15 terms each n-step Fibonacci(n) series
where n is drawn from [2..8]
'''
print('\n\n'.join([
fShow(*x) for x in [
(
'terms of the Jacobsthal sequence',
30, jacobsthal()),
(
'Jacobsthal-Lucas numbers',
30, jacobsthalish(2, 1)
),
(
'Jacobsthal oblong numbers',
20, map(
mul, jacobsthal(),
drop(1)(jacobsthal())
)
),
(
'primes in the Jacobsthal sequence',
10, filter(isPrime, jacobsthal())
)
]
]))
# fShow :: (String, Int, [Integer]) -> String
def fShow(k, n, xs):
'''N tabulated terms of XS, prefixed by the label K
'''
return f'{n} {k}:\n' + spacedTable(
list(chunksOf(5)(
[str(t) for t in take(n)(xs)]
))
)
# ----------------------- GENERIC ------------------------
# drop :: Int -> [a] -> [a]
# drop :: Int -> String -> String
def drop(n):
'''The sublist of xs beginning at
(zero-based) index n.
'''
def go(xs):
if isinstance(xs, (list, tuple, str)):
return xs[n:]
else:
take(n)(xs)
return xs
return go
# isPrime :: Int -> Bool
def isPrime(n):
'''True if n is prime.'''
if n in (2, 3):
return True
if 2 > n or 0 == n % 2:
return False
if 9 > n:
return True
if 0 == n % 3:
return False
def p(x):
return 0 == n % x or 0 == n % (2 + x)
return not any(map(p, range(5, 1 + int(n ** 0.5), 6)))
# take :: Int -> [a] -> [a]
# take :: Int -> String -> String
def take(n):
'''The prefix of xs of length n,
or xs itself if n > length xs.
'''
def go(xs):
return (
xs[0:n]
if isinstance(xs, (list, tuple))
else list(islice(xs, n))
)
return go
# unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
def unfoldr(f):
'''Generic anamorphism.
A lazy (generator) list unfolded from a seed value by
repeated application of f until no residue remains.
Dual to fold/reduce.
f returns either None, or just (value, residue).
For a strict output value, wrap in list().
'''
def go(x):
valueResidue = f(x)
while None is not valueResidue:
yield valueResidue[0]
valueResidue = f(valueResidue[1])
return go
# ---------------------- FORMATTING ----------------------
# chunksOf :: Int -> [a] -> [[a]]
def chunksOf(n):
'''A series of lists of length n, subdividing the
contents of xs. Where the length of xs is not evenly
divisible, the final list will be shorter than n.
'''
def go(xs):
return (
xs[i:n + i] for i in range(0, len(xs), n)
) if 0 < n else None
return go
# spacedTable :: [[String]] -> String
def spacedTable(rows):
'''Tabulated stringification of rows'''
columnWidths = [
max([len(x) for x in col])
for col in zip(*rows)
]
return '\n'.join([
' '.join(
map(
lambda x, w: x.rjust(w, ' '),
row, columnWidths
)
)
for row in rows
])
# MAIN ---
if __name__ == '__main__':
main()

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Task/Jacobsthal-numbers/Quackery/jacobsthal-numbers.quackery Normal file
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[ 2 over ** -1 rot ** - 3 / ] is j ( n --> n )
[ 2 over ** -1 rot ** + ] is jl ( n --> n )
[ dup 1+ j swap j * ] is jo ( n --> n )
say "First 30 Jacobsthal numbers:"
cr
30 times [ i^ j echo sp ]
cr cr
say "First 30 Jacobsthal-Lucas numbers:"
cr
30 times [ i^ jl echo sp ]
cr cr
say "First 20 Jacobsthal oblong numbers:"
cr
20 times [ i^ jo echo sp ]
cr cr
say "First 10 Jacobsthal primes:"
cr
[] 0
[ dup j dup isprime iff
[ swap dip join ]
else drop
1+
over size 10 = until ]
drop
witheach [ echo sp ]

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Task/Jacobsthal-numbers/Raku/jacobsthal-numbers.raku Normal file
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my $jacobsthal = cache lazy 0, 1, * × 2 + * … *;
my $jacobsthal-lucas = lazy 2, 1, * × 2 + * … *;
say "First 30 Jacobsthal numbers:";
say $jacobsthal[^30].batch(5)».fmt("%9d").join: "\n";
say "\nFirst 30 Jacobsthal-Lucas numbers:";
say $jacobsthal-lucas[^30].batch(5)».fmt("%9d").join: "\n";
say "\nFirst 20 Jacobsthal oblong numbers:";
say (^∞).map( { $jacobsthal[$_] × $jacobsthal[$_+1] } )[^20].batch(5)».fmt("%11d").join: "\n";
say "\nFirst 20 Jacobsthal primes:";
say $jacobsthal.grep( &is-prime )[^20].join: "\n";

52
Task/Jacobsthal-numbers/Red/jacobsthal-numbers.red Normal file
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Red ["Jacobsthal numbers"]
jacobsthal: function [n] [to-integer (2 ** n - (-1 ** n) / 3)]
lucas: function [n] [2 ** n + (-1 ** n)]
oblong: function [n] [
first split mold multiply to-float jacobsthal n to-float jacobsthal n + 1 #"." ; work around integer overflow
]
prime?: function [
"Returns true if the input is a prime number"
n [number!] "An integer to check for primality"
][
if 2 = n [return true]
if any [1 = n even? n] [return false]
limit: sqrt n
candidate: 3
while [candidate < limit][
if n % candidate = 0 [return false]
candidate: candidate + 2
]
true
]
show: function [n fn][
cols: length? mold fn n
repeat i n [
prin [pad fn subtract i 1 cols]
if i % 5 = 0 [prin newline]
]
prin newline
]
print "First 30 Jacobsthal numbers:"
show 30 :jacobsthal
print "First 30 Jacobsthal-Lucas numbers:"
show 30 :lucas
print "First 20 Jacobsthal oblong numbers:"
show 20 :oblong
print "First 10 Jacobsthal primes:"
primes: n: 0
while [primes < 10][
if prime? jacobsthal n [
print jacobsthal n
primes: primes + 1
]
n: n + 1
]

21
Task/Jacobsthal-numbers/Ruby/jacobsthal-numbers.rb Normal file
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require 'prime'
def jacobsthal(n) = (2**n + n[0])/3
def jacobsthal_lucas(n) = 2**n + (-1)**n
def jacobsthal_oblong(n) = jacobsthal(n) * jacobsthal(n+1)
puts "First 30 Jacobsthal numbers:"
puts (0..29).map{|n| jacobsthal(n) }.join(" ")
puts "\nFirst 30 Jacobsthal-Lucas numbers: "
puts (0..29).map{|n| jacobsthal_lucas(n) }.join(" ")
puts "\nFirst 20 Jacobsthal-Oblong numbers: "
puts (0..19).map{|n| jacobsthal_oblong(n) }.join(" ")
puts "\nFirst 10 prime Jacobsthal numbers: "
res = (0..).lazy.filter_map do |i|
j = jacobsthal(i)
j if j.prime?
end
puts res.take(10).force.join(" ")

47
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// [dependencies]
// rug = "0.3"
use rug::integer::IsPrime;
use rug::Integer;
fn jacobsthal_numbers() -> impl std::iter::Iterator<Item = Integer> {
(0..).map(|x| ((Integer::from(1) << x) - if x % 2 == 0 { 1 } else { -1 }) / 3)
}
fn jacobsthal_lucas_numbers() -> impl std::iter::Iterator<Item = Integer> {
(0..).map(|x| (Integer::from(1) << x) + if x % 2 == 0 { 1 } else { -1 })
}
fn jacobsthal_oblong_numbers() -> impl std::iter::Iterator<Item = Integer> {
let mut jn = jacobsthal_numbers();
let mut n0 = jn.next().unwrap();
std::iter::from_fn(move || {
let n1 = jn.next().unwrap();
let result = Integer::from(&n0 * &n1);
n0 = n1;
Some(result)
})
}
fn jacobsthal_primes() -> impl std::iter::Iterator<Item = Integer> {
jacobsthal_numbers().filter(|x| x.is_probably_prime(30) != IsPrime::No)
}
fn main() {
println!("First 30 Jacobsthal Numbers:");
for (i, n) in jacobsthal_numbers().take(30).enumerate() {
print!("{:9}{}", n, if (i + 1) % 5 == 0 { "\n" } else { " " });
}
println!("\nFirst 30 Jacobsthal-Lucas Numbers:");
for (i, n) in jacobsthal_lucas_numbers().take(30).enumerate() {
print!("{:9}{}", n, if (i + 1) % 5 == 0 { "\n" } else { " " });
}
println!("\nFirst 20 Jacobsthal oblong Numbers:");
for (i, n) in jacobsthal_oblong_numbers().take(20).enumerate() {
print!("{:11}{}", n, if (i + 1) % 5 == 0 { "\n" } else { " " });
}
println!("\nFirst 20 Jacobsthal primes:");
for n in jacobsthal_primes().take(20) {
println!("{}", n);
}
}

19
Task/Jacobsthal-numbers/Sidef/jacobsthal-numbers.sidef Normal file
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func jacobsthal(n) {
lucasU(1, -2, n)
}
func lucas_jacobsthal(n) {
lucasV(1, -2, n)
}
say "First 30 Jacobsthal numbers:"
say 30.of(jacobsthal)
say "\nFirst 30 Jacobsthal-Lucas numbers:"
say 30.of(lucas_jacobsthal)
say "\nFirst 20 Jacobsthal oblong numbers:"
say 21.of(jacobsthal).cons(2, {|a,b| a * b })
say "\nFirst 20 Jacobsthal primes:";
say (1..Inf -> lazy.map(jacobsthal).grep{.is_prime}.first(20))

59
Task/Jacobsthal-numbers/V-(Vlang)/jacobsthal-numbers.v Normal file
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import math.big
fn jacobsthal(n u32) big.Integer {
mut t := big.one_int
t=t.lshift(n)
mut s := big.one_int
if n%2 != 0 {
s=s.neg()
}
t -= s
return t/big.integer_from_int(3)
}
fn jacobsthal_lucas(n u32) big.Integer {
mut t := big.one_int
t=t.lshift(n)
mut a := big.one_int
if n%2 != 0 {
a=a.neg()
}
return t+a
}
fn main() {
mut jac := []big.Integer{len: 30}
println("First 30 Jacobsthal numbers:")
for i := u32(0); i < 30; i++ {
jac[i] = jacobsthal(i)
print("${jac[i]:9} ")
if (i+1)%5 == 0 {
println('')
}
}
println("\nFirst 30 Jacobsthal-Lucas numbers:")
for i := u32(0); i < 30; i++ {
print("${jacobsthal_lucas(i):9} ")
if (i+1)%5 == 0 {
println('')
}
}
println("\nFirst 20 Jacobsthal oblong numbers:")
for i := u32(0); i < 20; i++ {
print("${jac[i]*jac[i+1]:11} ")
if (i+1)%5 == 0 {
println('')
}
}
/*println("\nFirst 20 Jacobsthal primes:")
for n, count := u32(0), 0; count < 20; n++ {
j := jacobsthal(n)
if j.probably_prime(10) {
println(j)
count++
}
}*/
}

33
Task/Jacobsthal-numbers/Wren/jacobsthal-numbers.wren Normal file
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import "./big" for BigInt
import "./seq" for Lst
import "./fmt" for Fmt
var jacobsthal = Fn.new { |n| ((BigInt.one << n) - ((n%2 == 0) ? 1 : -1)) / 3 }
var jacobsthalLucas = Fn.new { |n| (BigInt.one << n) + ((n%2 == 0) ? 1 : -1) }
System.print("First 30 Jacobsthal numbers:")
var js = (0..29).map { |i| jacobsthal.call(i) }.toList
for (chunk in Lst.chunks(js, 5)) Fmt.print("$,12i", chunk)
System.print("\nFirst 30 Jacobsthal-Lucas numbers:")
var jsl = (0..29).map { |i| jacobsthalLucas.call(i) }.toList
for (chunk in Lst.chunks(jsl, 5)) Fmt.print("$,12i", chunk)
System.print("\nFirst 20 Jacobsthal oblong numbers:")
var oblongs = (0..19).map { |i| js[i] * js[i+1] }.toList
for (chunk in Lst.chunks(oblongs, 5)) Fmt.print("$,14i", chunk)
var primes = js.where { |j| j.isProbablePrime(10) }.toList
var count = primes.count
var i = 31
while (count < 20) {
var j = jacobsthal.call(i)
if (j.isProbablePrime(10)) {
primes.add(j)
count = count + 1
}
i = i + 1
}
System.print("\nFirst 20 Jacobsthal primes:")
for (i in 0..19) Fmt.print("$i", primes[i])

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Task/Jacobsthal-numbers/XPL0/jacobsthal-numbers.xpl0 Normal file
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func IsPrime(N); \Return 'true' if N is prime
int N, I;
[if N <= 2 then return N = 2;
if (N&1) = 0 then \even >2\ return false;
for I:= 3 to sqrt(N) do
[if rem(N/I) = 0 then return false;
I:= I+1;
];
return true;
];
proc Jaco(J2); \Display 30 Jacobsthal (or -Lucas) numbers
real J2, J1, J;
int N;
[RlOut(0, J2);
J1:= 1.0;
RlOut(0, J1);
for N:= 2 to 30-1 do
[J:= J1 + 2.0*J2;
RlOut(0, J);
if rem((N+1)/5) = 0 then CrLf(0);
J2:= J1; J1:= J;
];
CrLf(0);
];
real J, J1, J2, JO;
int N;
[Format(14, 0);
Jaco(0.0);
Jaco(2.0);
J2:= 1.0;
RlOut(0, 0.0);
J1:= 1.0;
RlOut(0, J1);
for N:= 2 to 20-1 do
[J:= (J1 + 2.0*J2);
JO:= J*J1;
RlOut(0, JO);
if rem((N+1)/5) = 0 then CrLf(0);
J2:= J1; J1:= J;
];
CrLf(0);
J2:= 0.0; J1:= 1.0; N:= 0;
loop [J:= J1 + 2.0*J2;
if IsPrime(fix(J)) then
[RlOut(0, J);
N:= N+1;
if rem(N/5) = 0 then CrLf(0);
if N >= 10 then quit;
];
J2:= J1; J1:= J;
];
]