Pisano period: Difference between revisions

{{trans|Nim}}

 

R m I/ gcd(m, n) * n

 

print(‘pisano(n) for integers 'n' from 1 to 180 are:’)

L(n) 1..180

 

{{out}}

168 336 48 364 180 72 264 348 168 400 120 232 132 178 120

</pre>

 

=={{header|Factor}}==

{{works with|Factor|0.99 2020-01-23}}

math.primes math.primes.factors math.ranges sequences ;

 

"n pisano for integers 'n' from 2 to 180:" print

2 180 [a,b] [ pisano ] map 15 group

{{out}}

<pre style="height:45ex">

 

=={{header|Go}}==

 

import "fmt"

}

fmt.Println()

 

{{out}}

 

=={{header|Haskell}}==

 

main = do

pisanoConjecture m = foldl1 lcm . map (uncurry pisanoPrime') $ factor m

where

{{out}}

<pre>PisanoPrime(p,2) for prime p lower than 15

Use efficient algorithm to calculate period.

 

import java.util.ArrayList;

import java.util.Collections;

 

}

{{out}}

<pre>

48 216 328 120 40 168 336 48 364 180

72 264 348 168 400 120 232 132 178 120

</pre>

 

=={{header|Julia}}==

 

const pisanos = Dict{Int, Int}()

println("\nPisano(n) for n from 2 to 180:\n", [pisano(i) for i in 2:180])

println("\nPisano(n) using pisanoPrime for n from 2 to 180:\n", [pisanotask(i) for i in 2:180])

<pre>

pisanoPrime(2, 2) = 6

[3, 8, 6, 20, 24, 16, 12, 24, 60, 10, 24, 28, 48, 40, 24, 36, 24, 18, 60, 16, 30, 48, 24, 100, 84, 72, 48, 14, 120, 30, 48, 40, 36, 80, 24, 76, 18, 56, 60, 40, 48, 88, 30, 120, 48, 32, 24, 112, 300, 72, 84, 108, 72, 20, 48, 72, 42, 58, 120, 60, 30, 48, 96, 140, 120, 136, 36, 48, 240, 70, 24, 148, 228, 200, 18, 80, 168, 78, 120, 216, 120, 168, 48, 180, 264, 56, 60, 44, 120, 112, 48, 120, 96, 180, 48, 196, 336, 120, 300, 50, 72, 208, 84, 80, 108, 72, 72, 108, 60, 152, 48, 76, 72, 240, 42, 168, 174, 144, 120, 110, 60, 40, 30, 500, 48, 256, 192, 88, 420, 130, 120, 144, 408, 360, 36, 276, 48, 46, 240, 32, 210, 140, 24, 140, 444, 112, 228, 148, 600, 50, 36, 72, 240, 60, 168, 316, 78, 216, 240, 48, 216, 328, 120, 40, 168, 336, 48, 364, 180, 72, 264, 348, 168, 400, 120, 232, 132, 178, 120]

</pre>

 

=={{header|Nim}}==

{{trans|Go}}

 

func primes(n: Positive): seq[int] =

echo "pisano(n) for integers 'n' from 1 to 180 are:"

for n in 1..180:

 

{{out}}

50 36 72 240 60 168 316 78 216 240 48 216 328 120 40

168 336 48 364 180 72 264 348 168 400 120 232 132 178 120</pre>

 

=={{header|Perl}}==

{{trans|Sidef}}

{{libheader|ntheory}}

use warnings;

use feature 'say';

say "Pisano periods for squares of primes p <= 50:\n", display( map { pisano_period_pp($_, 2) } @{primes(1, 50)} ),

"\nPisano periods for primes p <= 180:\n", display( map { pisano_period_pp($_, 1) } @{primes(1, 180)} ),

{{out}}

<pre>Pisano periods for squares of primes p <= 50:

 

=={{header|Phix}}==

{{out}}

<pre>

Uses the [[wp:SymPy|SymPy]] library.

 

from functools import reduce

 

print("\nPisano period (p) for integers 1 to 180")

for i in range(1, 181):

 

{{out}}

48 216 328 120 40 168 336 48 364 180

72 264 348 168 400 120 232 132 178 120</pre>

 

=={{header|Raku}}==

{{works with|Rakudo|2020.02}}

Didn't bother making two differently named routines, just made a multi that will auto dispatch to the correct candidate.

 

constant @fib := 1,1,*+*…*;

 

put "\nPisano period (p, 1) for integers 1 to 180";

{{out}}

<pre>Pisano period (p, 2) for primes less than 50

 

=={{header|REXX}}==

numeric digits 500 /*ensure enough decimal digits for Fib.*/

parse arg lim.1 lim.2 lim.3 . /*obtain optional arguments from the CL*/

end /*k*/; @.m= k; return k

/*──────────────────────────────────────────────────────────────────────────────────────*/

{{out|output|text=&nbsp; when using the default inputs:}}

 

32 210 140 24 140 444 112 228 148 600 50 36 72 240 60 168 316 78 216 240

48 216 328 120 40 168 336 48 364 180 72 264 348 168 400 120 232 132 178 120

</pre>

 

=={{header|Sidef}}==

 

assert(k.is_pos, "k = #{k} must be positive")

 

say "\nPisano periods for integers n from 1 to 180:"

{{out}}

<pre>

 

By assuming that '''Wall-Sun-Sun primes''' do not exist, we can compute the Pisano period more efficiently, as illustrated below on Fermat numbers '''F_n = 2^(2^n) + 1''':

(p - kronecker(5, p)).divisors.first_by {|d| fibmod(d, p) == 0 } * p**(k-1)

}

for k in (1..8) {

say ("Pisano(F_#{k}) = ", pisano_period(2**(2**k) + 1))

{{out}}

<pre>

{{libheader|Wren-math}}

{{libheader|Wren-fmt}}

 

// Calculates the Pisano period of 'm' from first principles.

if (n != 1 && n%15 == 0) System.print()

}

 

{{out}}

=={{header|zkl}}==

{{libheader|GMP}} GNU Multiple Precision Arithmetic Library for prime testing

 

fcn pisanoPeriod(p){

_assert_(BI(p).probablyPrime(), "%s is not a prime number".fmt(p));

pisanoPeriod(p.pow(k))

[1..50].pump(List,BI,"probablyPrime",Void.Filter, pisanoPrime.fp1(2))

.concat(" "," ").println();

println("Pisano period (p, 1) for primes less than 180:");

[1..180].pump(List,BI,"probablyPrime",Void.Filter, pisanoPrime.fp1(1))

{{out}}

<pre>

256 130 276 46 148 50 316 328 336 348 178

</pre>

primeFactors(m).pump(Dictionary().incV) //18 --> (2,3,3) --> ("2":1, "3":2)

.reduce(fcn(z,[(k,v])){ lcm(z,pisanoPrime(k.toInt(),v)) },1)

if(n!=m) acc.append(n/m); // opps, missed last factor

else acc;

[1..180].pump(List, pisano, "%4d".fmt)

{{out}}

<pre>