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2
Task/Sisyphus-sequence/00-META.yaml
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2
Task/Sisyphus-sequence/00-META.yaml
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---
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from: http://rosettacode.org/wiki/Sisyphus_sequence
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40
Task/Sisyphus-sequence/00-TASK.txt
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40
Task/Sisyphus-sequence/00-TASK.txt
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The '''Sisyphus sequence''' is an infinite sequence of positive integers that was devised in 2022 by Eric Angelini and Carole Dubois.
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The first term is 1. Subsequent terms are found by applying the following rule:
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* If the previous term was even, then halve it.
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* If the previous term was odd, then add the smallest prime number that has not yet been added.
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1 is odd and so the second term is: 1 + 2 = 3, because 2 is the smallest prime not yet added.
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3 is odd and so the third term is: 3 + 3 = 6, because 3 is the smallest prime not yet added.
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6 is even and so the fourth term is : 6 ÷ 2 = 3, and so on.
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;Task
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Find and show on this page (in 10 lines of 10 terms), the first 100 terms of the sequence.
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What are the '''1,000'''th, '''10,000'''th, '''100,000'''th and '''1,000,000'''th terms of the sequence and, in each case, what is the highest prime needed to reach them?
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If it is difficult or impossible for your language or output device to meet all of these requirements, then just do what you reasonably can.
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;Stretch
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What are the '''10 millionth''' and '''100 millionth''' terms and the highest prime needed to reach each one?
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By the time the '''100 millionth''' term is reached, which number(s) '''under 250''':
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* Have not yet occurred in the sequence.
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* Have occurred the most times and their number of occurrences.
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;Extreme stretch
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What is the number of the first term to equal 36?
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This was originally set as a challenge by Neil Sloane who was worried by its non-appearance and found by Russ Cox.
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;References
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* OEIS sequence [[oeis:A350877|A350877: The Sisyphus sequence]]
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<br>
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100
Task/Sisyphus-sequence/ALGOL-68/sisyphus-sequence.alg
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100
Task/Sisyphus-sequence/ALGOL-68/sisyphus-sequence.alg
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BEGIN # generate elements of the Sysiphus Sequence: see OEIS A350877 #
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# returns the largest element in a #
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OP MAX = ( []INT a )INT:
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IF LWB a >UPB a THEN 0
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ELSE
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INT result := a[ LWB a ];
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FOR i FROM LWB a + 1 TO UPB a DO
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IF result < a[ i ] THEN result := a[ i ] FI
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OD;
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result
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FI # MAX # ;
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# sieve the primes #
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INT sieve max = 1 000 000 000; ### CHANGE TO E.G.: 100 000 000 FOR ALGOL 68G ###
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BOOL is odd := TRUE;
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[ sieve max ]BOOL sieve; FOR i TO UPB sieve DO sieve[ i ] := is odd; is odd := NOT is odd OD;
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sieve[ 1 ] := FALSE;
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sieve[ 2 ] := TRUE;
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FOR s FROM 3 BY 2 TO ENTIER sqrt( sieve max ) DO
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IF sieve[ s ] THEN
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FOR p FROM s * s BY s TO sieve max DO sieve[ p ] := FALSE OD
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FI
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OD;
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[ 1 : 250 ]INT pos; # positions of 1..250 in the sequence #
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[ 1 : 250 ]INT occurs; # occurances of 1..250 in the sequence #
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FOR i TO UPB pos DO pos[ i ] := occurs[ i ] := 0 OD;
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INT max count = sieve max OVER 10; # highest element required #
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INT s := 1; # the first element is defined as 1 #
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INT count := 1; # count of elements found so far #
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print( ( "Sysiphus sequence - first 100 elements:", newline ) );
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print( ( whole( s, -4 ) ) );
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pos[ s ] := count;
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INT next to show := 1000; # next power-of-10 element to show #
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INT last used prime := 0; # latest prime from the list #
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INT p pos := 0; # current position in the sieve #
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WHILE count < max count DO
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# calculate the next element #
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IF NOT ODD s THEN
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# the previous element was even - halve it #
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s OVERAB 2
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ELSE
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# the previous element was odd: add the next prime from the list #
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WHILE p pos +:= 1;
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NOT sieve[ p pos ]
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DO SKIP OD;
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s +:= ( last used prime := p pos )
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FI;
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count +:= 1;
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IF count <= 100 THEN # have one of the first 100 elements #
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print( ( whole( s, -4 ) ) );
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IF count MOD 10 = 0 THEN print( ( newline ) ) FI;
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IF count = 100 THEN print( ( newline ) ) FI
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ELIF count = next to show THEN
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# reached a power of ten count #
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print( ( "sequence element ", whole( count, -10 )
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, " is ", whole( s, -10 )
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, ", highest used prime is ", whole( last used prime, -10 )
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, newline
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)
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);
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next to show *:= 10
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FI;
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IF s < UPB pos THEN
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IF pos[ s ] = 0 THEN
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# have the first appearence of s in the sequence #
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pos[ s ] := count
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FI;
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occurs[ s ] +:= 1
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FI
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OD;
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print( ( newline ) );
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print( ( "Integers in 1..", whole( UPB pos, 0 )
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, " not found in the sequence up to element ", whole( max count, 0 )
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, ":", newline
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)
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);
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FOR i TO UPB pos DO
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IF pos[ i ] = 0 THEN print( ( " ", whole( i, 0 ) ) ) FI
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OD;
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print( ( newline ) );
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INT max occurs = MAX occurs;
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print( ( "Integers in 1..", whole( UPB pos, 0 )
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, " that occur most often ( ", whole( max occurs, 0 )
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, " times ) up to element ", whole( max count, 0 )
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, ":", newline
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)
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);
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FOR i TO UPB occurs DO
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IF occurs[ i ] = max occurs THEN print( ( " ", whole( i, 0 ) ) ) FI
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OD;
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print( ( newline, newline ) );
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print( ( "Position in the sequence of 1..100 up to element ", whole( max count, 0 )
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, ":", newline
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)
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);
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FOR i TO 100 DO
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print( ( IF pos[ i ] = 0 THEN " unknown" ELSE whole( pos[ i ], -8 ) FI ) );
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IF i MOD 8 = 0 THEN print( ( newline ) ) FI
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OD
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END
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13
Task/Sisyphus-sequence/J/sisyphus-sequence-1.j
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13
Task/Sisyphus-sequence/J/sisyphus-sequence-1.j
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sisyphuseq=: {{
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r=. 1
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P=: _1
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while. y>#r do. p=. {:P
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if. 2|N=. {:r do.
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P=: P, p=. 1+p
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r=. r,N+p:p
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else.
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P=: P, p
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r=. r,-:N
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end.
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end.
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}}
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17
Task/Sisyphus-sequence/J/sisyphus-sequence-2.j
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Task/Sisyphus-sequence/J/sisyphus-sequence-2.j
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seq=: sisyphuseq 1e6
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10 10$seq NB. first 100 members of sequence
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1 3 6 3 8 4 2 1 8 4
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2 1 12 6 3 16 8 4 2 1
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18 9 28 14 7 30 15 44 22 11
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42 21 58 29 70 35 78 39 86 43
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96 48 24 12 6 3 62 31 92 46
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23 90 45 116 58 29 102 51 130 65
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148 74 37 126 63 160 80 40 20 10
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5 106 53 156 78 39 146 73 182 91
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204 102 51 178 89 220 110 55 192 96
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48 24 12 6 3 142 71 220 110 55
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x:(,. (seq {~ <:),. P p:@{~ <:) 1e3 1e4 1e5 1e6 NB. nth elements of sequence and corresponding largest prime used
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1000 990 2273
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10000 24975 30713
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100000 265781 392111
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1000000 8820834 4761697
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26
Task/Sisyphus-sequence/Jq/sisyphus-sequence-1.jq
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26
Task/Sisyphus-sequence/Jq/sisyphus-sequence-1.jq
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# The def of _nwise can be omitted if using the C implementation of jq.
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def _nwise($n):
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def n: if length <= $n then . else .[0:$n] , (.[$n:] | n) end;
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n;
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def lpad($len): tostring | ($len - length) as $l | (" " * $l) + .;
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# tabular print
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def tprint(columns; wide):
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reduce _nwise(columns) as $row ("";
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. + ($row|map(lpad(wide)) | join(" ")) + "\n" );
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# Input: a positive integer
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# Output: an array, $a, of length .+1 such that
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# $a[$i] is $i if $i is prime, and false otherwise.
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def primeSieve:
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# erase(i) sets .[i*j] to false for integral j > 1
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def erase($i):
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if .[$i] then
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reduce (range(2*$i; length; $i)) as $j (.; .[$j] = false)
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else .
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end;
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(. + 1) as $n
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| (($n|sqrt) / 2) as $s
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| [null, null, range(2; $n)]
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| reduce (2, 1 + (2 * range(1; $s))) as $i (.; erase($i)) ;
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42
Task/Sisyphus-sequence/Jq/sisyphus-sequence-2.jq
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42
Task/Sisyphus-sequence/Jq/sisyphus-sequence-2.jq
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# $limit is the target number of Sisyphus numbers to find and should be at least 100
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def task($limit):
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((7 * $limit) | primeSieve | map(select(.))) as $primes
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| { under250: [0, 1],
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sisyphus: [1],
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prev: 1,
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nextPrimeIndex: 0,
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specific: 1000,
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count:1 }
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| while(.count <= $limit;
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.emit = null
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| if .prev % 2 == 0 then .next = .prev/2
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else .next = .prev + $primes[.nextPrimeIndex]
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| .nextPrimeIndex += 1
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end
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| .count += 1
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| if .count <= 100 then .sisyphus += [.next] else . end
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| if .next < 250 then .under250[.next] += 1 else . end
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| if .count == 100
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then .emit = "The first 100 members of the Sisyphus sequence are:\n" + (.sisyphus | tprint(10;3))
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elif .count == .specific
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then $primes[.nextPrimeIndex-1] as $prime
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| .emit = "\(.count|lpad(8))th member is: \(.next|lpad(10)) and highest prime needed: \($prime|lpad(10))"
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| .specific *= 10
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else .
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end
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| .prev = .next )
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# The results:
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| select(.emit).emit,
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if .count == $limit
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then .under250 as $u
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| [range(1;250) | select( $u[.] == null)] as $notFound
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| ($u|max) as $max
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| [range(1;250) | select($u[.] == $max)] as $maxFound
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| "\nThese numbers under 250 do not occur in the first \(.count) terms:",
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" \($notFound)",
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"\nThese numbers under 250 occur the most in the first \(.count) terms:",
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" \($maxFound) all occur \($max) times."
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else empty
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end;
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task(1e7)
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61
Task/Sisyphus-sequence/Julia/sisyphus-sequence.julia
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61
Task/Sisyphus-sequence/Julia/sisyphus-sequence.julia
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using Counters, Formatting, Primes
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struct Sisyphus end
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function Base.iterate(s::Sisyphus, state = (0, 0))
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n, p = state
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if n == 0
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return (1, 0), (1, 0)
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else
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if isodd(n)
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p = nextprime(p + 1)
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n += p
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else
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n ÷= 2
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end
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return (n, p), (n, p)
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end
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end
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function test_sisyphus()
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coun = Counter{Int}()
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println("The first 100 members of the Sisyphus sequence are:")
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for (i, (n, p)) in enumerate(Sisyphus())
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if n < 250
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coun[n] += 1
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end
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if i < 101
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print(rpad(n, 4), i % 10 == 0 ? "\n" : "")
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elseif i in [1000, 10000, 100_000, 1_000_000, 10_000_000, 100_000_000]
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print(
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rpad("\n$(format(i, commas = true))th number:", 22),
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rpad(format(n, commas = true), 14),
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"Highest prime needed: ",
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format(p, commas = true),
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)
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end
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if i == 100_000_000
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println(
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"\n\nThese numbers under 250 do not occur in the first 100,000,000 terms:",
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)
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println(" ", filter(j -> !haskey(coun, j), 1:249), "\n")
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sorteds = sort!([(p, coun[p]) for p in coun], by = last)
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maxtimes = sorteds[end][2]
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println(
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"These numbers under 250 occur the most ($maxtimes times) in the first 100,000,000 terms:",
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)
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println(" ", map(first, filter(p -> p[2] == maxtimes, sorteds)))
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elseif n == 36
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println("\nLocating the first entry in the sequence with value 36:")
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println(
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" The sequence position: ",
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format(i, commas = true),
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" has value $n using prime ",
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format(p, commas = true),
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)
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break
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end
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end
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end
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test_sisyphus()
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89
Task/Sisyphus-sequence/Nim/sisyphus-sequence.nim
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89
Task/Sisyphus-sequence/Nim/sisyphus-sequence.nim
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@ -0,0 +1,89 @@
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import std/[bitops, math, strformat, strutils, tables]
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# Sieve which uses only one bit for odd integers.
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type Sieve = object
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data: seq[byte]
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func `[]`(sieve: Sieve; idx: Positive): bool =
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## Return value of element at index "idx".
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let idx = idx shr 1
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let iByte = idx shr 3
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let iBit = idx and 7
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result = sieve.data[iByte].testBit(iBit)
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func `[]=`(sieve: var Sieve; idx: Positive; val: bool) =
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## Set value of element at index "idx".
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let idx = idx shr 1
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let iByte = idx shr 3
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let iBit = idx and 7
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if val: sieve.data[iByte].setBit(iBit)
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else: sieve.data[iByte].clearBit(iBit)
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func initSieve(lim: Positive): Sieve =
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## Initialize a sieve from 2 to "lim".
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result.data = newSeq[byte]((lim + 16) shr 4)
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result[1] = true
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for n in countup(3, sqrt(lim.toFloat).int, 2):
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if not result[n]:
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for k in countup(n * n, lim, 2 * n):
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result[k] = true
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func isPrime(sieve: Sieve; n: int): bool =
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## Return true if "n" is prime.
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result = if (n and 1) == 0: n == 2 else: not sieve[n]
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let sieve = initSieve(700_000_000)
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func nextPrime(sieve: Sieve; n: int): int =
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## Return next prime greater than "n".
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result = n
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while true:
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inc result
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if sieve.isPrime(result):
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return
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var p = 0 # Current prime (none for now).
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var count = 0 # Count of elements in sequence.
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var n = 1 # Last element of sequence.
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var counts: CountTable[int] # Count of occurrences for value < 250.
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echo "First 100 terms of the Sisyphus sequence:"
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while count < 100_000_000:
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# Process current number.
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inc count
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if count <= 100:
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stdout.write &"{n:3}"
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stdout.write if count mod 10 == 0: '\n' else: ' '
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if count == 100: echo()
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elif count in [1_000, 10_000, 100_000, 1_000_000, 10_000_000, 100_000_000]:
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echo &"The {insertSep($count)}th term is {insertSep($n)} " &
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&"and the highest prime needed is {insertSep($p)}."
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# Update count table.
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if n < 250: counts.inc(n)
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# Find next term of the sequence.
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if (n and 1) == 0:
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n = n shr 1
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else:
|
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p = sieve.nextPrime(p)
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inc n, p
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|
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echo()
|
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echo "Numbers under 250 which don’t occur in the first 100_000_000 terms:"
|
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for n in 1..249:
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if n notin counts:
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stdout.write " ", n
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echo '\n'
|
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|
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echo "Numbers under 250 which occur the most in the first 100_000_000 terms:"
|
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counts.sort()
|
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let largest = counts.largest[1]
|
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for (n, count) in counts.pairs:
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if count == largest:
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stdout.write " ", n
|
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else:
|
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# No more value with the largest number of occurrences.
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echo()
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break
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35
Task/Sisyphus-sequence/Perl/sisyphus-sequence.pl
Normal file
35
Task/Sisyphus-sequence/Perl/sisyphus-sequence.pl
Normal file
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|
@ -0,0 +1,35 @@
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use strict;
|
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use warnings;
|
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use feature 'say';
|
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|
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use ntheory 'next_prime';
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use List::Util <any max>;
|
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use integer;
|
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|
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sub comma { reverse ((reverse shift) =~ s/.{3}\K/,/gr) =~ s/^,//r }
|
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sub table { my $t = 10 * (my $c = 1 + length max @_); ( sprintf( ('%'.$c.'d')x@_, @_) ) =~ s/.{1,$t}\K/\n/gr }
|
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|
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my ($exp1, $exp2, $limit1, $limit2) = (3, 8, 100, 250);
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my ($n, $s0, $s1, $p, @S1, %S, %S2) = (1, 1, 0, 1, 1);
|
||||
my @Nth = map { 10**$_ } $exp1..$exp2;
|
||||
|
||||
do {
|
||||
$n++;
|
||||
$s1 = (0 == $s0%2) ? $s0/2 : $s0 + ($p = next_prime($p));
|
||||
push @S1, $s1 if $n <= $limit1;
|
||||
$S2{$s1}++ if $s1 <= $limit2;
|
||||
($S{$n}{'value'} = $s1 and $S{$n}{'prime'} = $p) if any { $_ == $n } @Nth;
|
||||
$s0 = $s1;
|
||||
} until $n == $Nth[-1];
|
||||
|
||||
say 'The first 100 members of the Sisyphus sequence are:';
|
||||
say table @S1;
|
||||
|
||||
printf "%12sth member is: %13s with prime: %11s\n", comma($_), comma($S{$_}{value}), comma($S{$_}{prime}) for @Nth;
|
||||
|
||||
printf "\nNumbers under $limit2 that do not occur in the first %s terms:\n", comma $Nth[-1];
|
||||
say join ' ', grep { ! defined $S2{$_} } 1..$limit2;
|
||||
|
||||
my $max = max values %S2;
|
||||
printf "\nNumbers under $limit2 occur the most ($max times) in the first %s terms:\n", comma $Nth[-1];
|
||||
say join ' ', sort { $a <=> $b } grep { $S2{$_} == $max } keys %S2;
|
||||
35
Task/Sisyphus-sequence/Phix/sisyphus-sequence-1.phix
Normal file
35
Task/Sisyphus-sequence/Phix/sisyphus-sequence-1.phix
Normal file
|
|
@ -0,0 +1,35 @@
|
|||
(phixonline)-->
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
|
||||
<span style="color: #008080;">constant</span> <span style="color: #000000;">limit</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1e8</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">sisyphus</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span>
|
||||
<span style="color: #000000;">under250</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">reinstate</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">250</span><span style="color: #0000FF;">),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">np</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">specific</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">m</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">next</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">even</span><span style="color: #0000FF;">(</span><span style="color: #000000;">next</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">next</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">2</span>
|
||||
<span style="color: #008080;">else</span>
|
||||
<span style="color: #000000;">np</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #000000;">next</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">get_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">np</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">next</span> <span style="color: #0000FF;"><=</span> <span style="color: #000000;">250</span> <span style="color: #008080;">then</span> <span style="color: #000000;">under250</span><span style="color: #0000FF;">[</span><span style="color: #000000;">next</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;"><=</span> <span style="color: #000000;">100</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">sisyphus</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">next</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">100</span> <span style="color: #008080;">then</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;">"The first 100 members of the Sisyphus sequence are:\n%s\n"</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sisyphus</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%3d"</span><span style="color: #0000FF;">)})</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">elsif</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">specific</span> <span style="color: #008080;">then</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;">"%,13d%s member is: %,13d and highest prime needed: %,11d\n"</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">ord</span><span style="color: #0000FF;">(</span><span style="color: #000000;">count</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">next</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">get_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">np</span><span style="color: #0000FF;">)})</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">limit</span> <span style="color: #008080;">then</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">largest</span><span style="color: #0000FF;">(</span><span style="color: #000000;">under250</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">);</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">specific</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">10</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</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;">"\nThese numbers under 250 do not occur in the first %,d terms:\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</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;">" %v\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">find_all</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">under250</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;">"\nThese numbers under 250 occur the most in the first %,d terms:\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</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;">" %v all occur %d times.\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">find_all</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #000000;">under250</span><span style="color: #0000FF;">),</span><span style="color: #000000;">m</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span>
|
||||
<!--
|
||||
28
Task/Sisyphus-sequence/Phix/sisyphus-sequence-2.phix
Normal file
28
Task/Sisyphus-sequence/Phix/sisyphus-sequence-2.phix
Normal file
|
|
@ -0,0 +1,28 @@
|
|||
(notonline)-->
|
||||
<span style="color: #008080;">without</span> <span style="color: #008080;">js</span>
|
||||
<span style="color: #008080;">include</span> <span style="color: #000000;">builtins</span><span style="color: #0000FF;">/</span><span style="color: #000000;">primesieve</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span> <span style="color: #000080;font-style:italic;">-- (can provide if desired, ask me on either my or this tasks talk page)</span>
|
||||
<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #004600;">WINDOWS</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #000000;">64</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">(),</span> <span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">np</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">next</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">next</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">36</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">even</span><span style="color: #0000FF;">(</span><span style="color: #000000;">next</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">next</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">2</span>
|
||||
<span style="color: #008080;">else</span>
|
||||
<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">primesieve_next_prime</span><span style="color: #0000FF;">()</span>
|
||||
<span style="color: #000000;">next</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">p</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()></span><span style="color: #000000;">t1</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">cpc</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">count</span><span style="color: #0000FF;">/</span><span style="color: #000000;">77_534_485_877</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #000000;">ppc</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">/</span><span style="color: #000000;">677_121_348_413</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">100</span>
|
||||
<span style="color: #7060A8;">progress</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"count: %,d (%2.2f%%) p: %,d (%2.2f%%)\r"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cpc</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ppc</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #7060A8;">progress</span><span style="color: #0000FF;">(</span><span style="color: #008000;">""</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;">"%,d%s member is: %,d and highest prime needed: %,d\n"</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">ord</span><span style="color: #0000FF;">(</span><span style="color: #000000;">count</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">next</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span>
|
||||
<!--
|
||||
73
Task/Sisyphus-sequence/Python/sisyphus-sequence-1.py
Normal file
73
Task/Sisyphus-sequence/Python/sisyphus-sequence-1.py
Normal file
|
|
@ -0,0 +1,73 @@
|
|||
from collections import Counter
|
||||
from itertools import islice
|
||||
from typing import Iterable
|
||||
from typing import Iterator
|
||||
from typing import Tuple
|
||||
from typing import TypeVar
|
||||
|
||||
import primesieve
|
||||
|
||||
|
||||
def primes() -> Iterator[int]:
|
||||
it = primesieve.Iterator()
|
||||
while True:
|
||||
yield it.next_prime()
|
||||
|
||||
|
||||
def sisyphus() -> Iterator[Tuple[int, int]]:
|
||||
prime = primes()
|
||||
n = 1
|
||||
p = 0
|
||||
yield n, p
|
||||
|
||||
while True:
|
||||
if n % 2:
|
||||
p = next(prime)
|
||||
n = n + p
|
||||
else:
|
||||
n = n // 2
|
||||
yield n, p
|
||||
|
||||
|
||||
def consume(it: Iterator[Tuple[int, int]], n) -> Tuple[int, int]:
|
||||
next(islice(it, n - 1, n - 1), None)
|
||||
return next(it)
|
||||
|
||||
|
||||
T = TypeVar("T")
|
||||
|
||||
|
||||
def batched(it: Iterable[T], n: int) -> Iterable[Tuple[T, ...]]:
|
||||
_it = iter(it)
|
||||
batch = tuple(islice(_it, n))
|
||||
while batch:
|
||||
yield batch
|
||||
batch = tuple(islice(_it, n))
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
it = sisyphus()
|
||||
first_100 = list(islice(it, 100))
|
||||
print("The first 100 members of the Sisyphus sequence are:")
|
||||
for row in batched(first_100, 10):
|
||||
print(" ".join(str(n).rjust(3) for n, _ in row))
|
||||
|
||||
print("")
|
||||
|
||||
for interval in [10**x for x in range(3, 9)]:
|
||||
n, prime = consume(it, interval - (interval // 10))
|
||||
print(f"{interval:11,}th number: {n:13,} highest prime needed: {prime:11,}")
|
||||
|
||||
print("")
|
||||
|
||||
sisyphus_lt_250 = Counter(n for n, _ in islice(sisyphus(), 10**8) if n < 250)
|
||||
print("These numbers under 250 do not occur in the first 100,000,000 terms:")
|
||||
print(" ", [n for n in range(1, 250) if n not in sisyphus_lt_250])
|
||||
print("")
|
||||
|
||||
most_common = sisyphus_lt_250.most_common(1)[0][1]
|
||||
print("These numbers under 250 occur the most in the first 100,000,000 terms:")
|
||||
print(
|
||||
f" {[n for n, c in sisyphus_lt_250.items() if c == most_common]} "
|
||||
f"all occur {most_common} times."
|
||||
)
|
||||
22
Task/Sisyphus-sequence/Python/sisyphus-sequence-2.py
Normal file
22
Task/Sisyphus-sequence/Python/sisyphus-sequence-2.py
Normal file
|
|
@ -0,0 +1,22 @@
|
|||
import primesieve
|
||||
|
||||
def sisyphus36():
|
||||
primes = primesieve.Iterator()
|
||||
n = 1
|
||||
p = 0
|
||||
i = 1
|
||||
|
||||
while True:
|
||||
i += 1
|
||||
if n % 2:
|
||||
p = primes.next_prime()
|
||||
n = n + p
|
||||
else:
|
||||
n = n // 2
|
||||
|
||||
if n == 36:
|
||||
print(f"{i:,}, {n:,}, {p:,}")
|
||||
break
|
||||
|
||||
if __name__ == "__main__":
|
||||
sisyphus36()
|
||||
25
Task/Sisyphus-sequence/Raku/sisyphus-sequence.raku
Normal file
25
Task/Sisyphus-sequence/Raku/sisyphus-sequence.raku
Normal file
|
|
@ -0,0 +1,25 @@
|
|||
use Math::Primesieve;
|
||||
use Lingua::EN::Numbers;
|
||||
|
||||
my ($exp1, $exp2, $limit1, $limit2) = 3, 8, 100, 250;
|
||||
my ($n, $s0, $s1, $p, @S1, %S) = 1, 1, Any, Any, 1;
|
||||
my $iterator = Math::Primesieve::iterator.new;
|
||||
my @Nth = ($exp1..$exp2)».exp(10);
|
||||
my $S2 = BagHash.new;
|
||||
|
||||
repeat {
|
||||
$n++;
|
||||
$s1 = $s0 %% 2 ?? $s0 div 2 !! $s0 + ($p = $iterator.next);
|
||||
@S1.push: $s1 if $n ≤ $limit1;
|
||||
$S2.add: $s1 if $s1 ≤ $limit2;
|
||||
%S{$n}{'value', 'prime'} = $s1, $p if $n ∈ @Nth;
|
||||
$s0 = $s1;
|
||||
} until $n == @Nth[*-1];
|
||||
|
||||
say "The first $limit1 members of the Sisyphus sequence are:";
|
||||
say @S1.batch(10)».fmt('%4d').join("\n") ~ "\n";
|
||||
printf "%12sth member is: %13s with prime: %11s\n", ($_, %S{$_}{'value'}, %S{$_}{'prime'})».&comma for @Nth;
|
||||
say "\nNumbers under $limit2 that do not occur in the first {comma @Nth[*-1]} terms:";
|
||||
say (1..$limit2).grep: * ∉ $S2.keys;
|
||||
say "\nNumbers under $limit2 that occur the most ({$S2.values.max} times) in the first {comma @Nth[*-1]} terms:";
|
||||
say $S2.keys.grep({ $S2{$_} == $S2.values.max}).sort;
|
||||
44
Task/Sisyphus-sequence/Wren/sisyphus-sequence-1.wren
Normal file
44
Task/Sisyphus-sequence/Wren/sisyphus-sequence-1.wren
Normal file
|
|
@ -0,0 +1,44 @@
|
|||
import "./math" for Int, Nums
|
||||
import "./fmt" for Fmt
|
||||
|
||||
var limit = 1e8
|
||||
var primes = Int.primeSieve(7 * limit)
|
||||
var under250 = List.filled(250, 0)
|
||||
var sisyphus = [1]
|
||||
under250[1] = 1
|
||||
var prev = 1
|
||||
var nextPrimeIndex = 0
|
||||
var specific = 1000
|
||||
var count = 1
|
||||
while (true) {
|
||||
var next
|
||||
if (prev % 2 == 0) {
|
||||
next = prev / 2
|
||||
} else {
|
||||
next = prev + primes[nextPrimeIndex]
|
||||
nextPrimeIndex = nextPrimeIndex + 1
|
||||
}
|
||||
count = count + 1
|
||||
if (count <= 100) sisyphus.add(next)
|
||||
if (next < 250) under250[next] = under250[next] + 1
|
||||
if (count == 100) {
|
||||
System.print("The first 100 members of the Sisyphus sequence are:")
|
||||
Fmt.tprint("$3d ", sisyphus, 10)
|
||||
System.print()
|
||||
} else if (count == specific) {
|
||||
var prime = primes[nextPrimeIndex-1]
|
||||
Fmt.print("$,13r member is: $,13d and highest prime needed: $,11d", count, next, prime)
|
||||
if (count == limit) {
|
||||
var notFound = (1..249).where { |i| under250[i] == 0 }.toList
|
||||
var max = Nums.max(under250)
|
||||
var maxFound = (1..249).where { |i| under250[i] == max }.toList
|
||||
Fmt.print("\nThese numbers under 250 do not occur in the first $,d terms:", count)
|
||||
Fmt.print(" $n", notFound)
|
||||
Fmt.print("\nThese numbers under 250 occur the most in the first $,d terms:", count)
|
||||
Fmt.print(" $n all occur $d times.", maxFound, max)
|
||||
return
|
||||
}
|
||||
specific = 10 * specific
|
||||
}
|
||||
prev = next
|
||||
}
|
||||
21
Task/Sisyphus-sequence/Wren/sisyphus-sequence-2.wren
Normal file
21
Task/Sisyphus-sequence/Wren/sisyphus-sequence-2.wren
Normal file
|
|
@ -0,0 +1,21 @@
|
|||
import "./psieve" for Primes
|
||||
import "./fmt" for Fmt
|
||||
|
||||
var it = Primes.iter()
|
||||
var n = 1
|
||||
var count = 1
|
||||
var prime
|
||||
var target = 36
|
||||
while (true) {
|
||||
if (n % 2 == 1) {
|
||||
prime = it.next
|
||||
n = n + prime
|
||||
} else {
|
||||
n = n / 2
|
||||
}
|
||||
count = count + 1
|
||||
if (n == target) {
|
||||
Fmt.print("$,r member is: $d and highest prime needed: $,d", count, target, prime)
|
||||
return
|
||||
}
|
||||
}
|
||||
Loading…
Add table
Add a link
Reference in a new issue