51 lines
2.1 KiB
Text
51 lines
2.1 KiB
Text
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do -- find some Jacobsthal and related Numbers
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local fmt = require( "fmt" ) -- RC Pluto formatting library
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local int = require( "int" ) -- RC Pluto integer library - inc. some prime utilities
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local maxJacobsthal <const> -- highest Jacobsthal number we will find
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, maxOblong <const> -- highest Jacobsthal oblong number we will find
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, maxJPrime <const> -- number of Jacobsthal primes we will find
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= 29, 20, 10
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local j <const> -- will hold Jacobsthal numbers
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, jl <const> -- will hold Jacobsthal-Lucas numbers
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, jo <const> -- will hold Jacobsthal oblong numbers
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= {}, {}, {}
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-- calculate the Jacobsthal Numbers and related numbers
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-- Jacobsthal : J0 == 0, J1 == 1, Jn == Jn-1 + 2 × Jn-2
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-- Jacobsthal-Lucas: JL0 == 2, JL1 == 1, JLn == JLn-1 + 2 × JLn-2
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-- Jacobsthal oblong: JOn == Jn x Jn-1
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-- Pluto arrays can be indexed from 0 but as jo is indexed from 1, we index j, jl and jo
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-- from 1 to simplify printing them
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j[ 1 ], j[ 2 ], jl[ 1 ], jl[ 2 ], jo[ 1 ] = 0, 1, 2, 1, 0
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for n = 2, maxJacobsthal do
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j[ n + 1 ] = j[ n ] + ( 2 * j[ n - 1 ] )
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jl[ n + 1 ] = jl[ n ] + ( 2 * jl[ n - 1 ] )
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end
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for n = 1, maxOblong do
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jo[ n ] = j[ n + 1 ] * j[ n ]
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end
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local function showNumbers( legend : string, numbers : table )
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fmt.write( "First %d %s\n", # numbers, legend )
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fmt.tprint( " %11d", numbers, 5, "", "" )
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end
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-- show the various numbers numbers
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showNumbers( "Jacobsthal Numbers:", j )
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showNumbers( "Jacobsthal-Lucas Numbers:", jl )
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showNumbers( "Jacobsthal oblong Numbers:", jo )
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-- find some prime Jacobsthal numbers
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fmt.write( "First %d Jacobstal primes:\n n Jn\n", maxJPrime )
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local jn1, jn2, pCount, n = j[ 2 ], j[ 1 ], 0, 2
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while pCount < maxJPrime do
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local jn <const> = jn1 + ( 2 * jn2 )
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jn2, jn1 = jn1, jn
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if int.isprime( jn ) then
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++ pCount
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fmt.write( "%4d: %d\n", n, jn )
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end
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++ n
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end
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end
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