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Pisano period: Difference between revisions

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Pisano period (view source)

Revision as of 19:19, 9 March 2024

11,969 bytes added ,  2 months ago
m
→‎{{header|EasyLang}}
(→‎{{header|Lua}}: remove ";")
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Line 537:
if m = 0
prims[] &= i
prims[]cnt &= 0
while m = 0
prims[-1]cnt += 1
n = d
d = n div i
m = n mod i
.
prims[] &= cnt
.
.
Line 1,429 ⟶ 1,430:
48 216 328 120 40 168 336 48 364 180
72 264 348 168 400 120 232 132 178 120
</pre>
 
=={{header|JavaScript}}==
{{Trans|Lua}}
<syntaxhighlight lang="javascript">
{ // find the Pisano period of some primes and composites
 
const maxNumber = 180
// sieve the primes to maxNumber
let isPrime = []
for( let i = 1; i <= maxNumber; i ++ ){ isPrime[ i ] = i % 2 != 0 }
isPrime[ 1 ] = false
isPrime[ 2 ] = true
const rootMaxNumber = Math.floor( Math.sqrt( maxNumber ) )
for( let s = 3; s <= rootMaxNumber; s += 2 )
{
if( isPrime[ s ] )
{
for( let p = s * s; p <= maxNumber; p += s ){ isPrime[ p ] = false }
}
}
 
function pisano( m ) // returns the Pisano period of m
{
let p = 0, c = 1
for( let i = 0; i < ( m * m ); i ++ )
{
[ p, c ] = [ c, ( p + c ) % m ]
if( p == 0 && c == 1 ){ return i + 1 }
}
return 1
}
 
// returns the Pisano period of p^k or 0 if p is not prime or k < 1
function pisanoPrime( p, k )
{
return ( ! isPrime[ p ] || k < 1 ) ? 0 : Math.floor( p ** ( k - 1 ) ) * pisano( p )
}
 
function d4( n ) // returns n formatted in 4 characcters
{
return n.toString().padStart( 4 )
}
 
console.log( "Pisano period of p^2 where p is a prime < 15:" )
let list = ""
for( let p = 1; p < 15; p ++ )
{
if( isPrime[ p ] ){ list += " " + p + ":" + pisanoPrime( p, 2 ) }
}
console.log( list )
console.log( "Pisano period of primes up to 180, non-primes shown as \"*\":" )
list = ""
for( p = 1; p <= 180; p ++ )
{
list += ( ! isPrime[ p ] ? " *" : d4( pisanoPrime( p, 1 ) ) )
if( p % 10 == 0 ){ list += "\n" }
}
console.log( list )
console.log( "Pisano period of positive integers up to 180:" )
list = ""
for( let n = 1; n <= 180; n ++ )
{
list += d4( pisano( n ) )
if( n % 10 == 0 ){ list += "\n" }
}
console.log( list )
 
}
</syntaxhighlight>
{{out}}
<pre>
Pisano period of p^2 where p is a prime < 15:
2:6 3:24 5:100 7:112 11:110 13:364
Pisano period of primes up to 180, non-primes shown as "*":
* 3 8 * 20 * 16 * * *
10 * 28 * * * 36 * 18 *
* * 48 * * * * * 14 *
30 * * * * * 76 * * *
40 * 88 * * * 32 * * *
* * 108 * * * * * 58 *
60 * * * * * 136 * * *
70 * 148 * * * * * 78 *
* * 168 * * * * * 44 *
* * * * * * 196 * * *
50 * 208 * * * 72 * 108 *
* * 76 * * * * * * *
* * * * * * 256 * * *
130 * * * * * 276 * 46 *
* * * * * * * * 148 *
50 * * * * * 316 * * *
* * 328 * * * 336 * * *
* * 348 * * * * * 178 *
 
Pisano period of positive integers up to 180:
1 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>
 
Line 1,541 ⟶ 1,655:
 
local function pisano( m ) -- returns the Pisano period of m
local p, c = 0, 1
local c = 1
local r = 0
for i = 0, ( m * m ) - 1 do
p, c = c, ( p + c ) % m
Line 1,621 ⟶ 1,733:
72 264 348 168 400 120 232 132 178 120
</pre>
 
 
=={{header|Mathematica}}/{{header|Wolfram Language}}==
{{trans|Julia}}
<syntaxhighlight>
ClearAll["Global`*"];
 
pisanos = <||>;
pisano[p_] := Module[{lastn, n, i}, If[p < 2, Return[1]];
i = pisanos[p];
If[i > 0, Return[i]];
lastn = 0; n = 1;
For[i = 1, i <= p^2, i++, {lastn, n} = {n, Mod[lastn + n, p]};
If[lastn == 0 && n == 1, pisanos[p] = i;
Return[i]]];
Return[1]]
 
pisanoprime[p_, k_] := Module[{}, Assert[PrimeQ[p]];
p^(k - 1)*pisano[p]]
 
pisanotask[n_] := Module[{factors}, factors = FactorInteger[n];
Map[pisanoprime[#[[1]], #[[2]]] &, factors] // Apply[LCM, #] &]
 
Do[If[PrimeQ[i],
Print["pisanoPrime[", i, ", 2] = ", pisanoprime[i, 2]]], {i, 1, 15}]
 
Do[If[PrimeQ[i],
Print["pisanoPrime[", i, ", 1] = ", pisanoprime[i, 1]]], {i, 1, 180}]
 
Print["\nPisano[n] for n from 2 to 180:"];
Print[Table[pisano[i], {i, 2, 180}]]
 
Print["\nPisano[n] using pisanoPrime for n from 2 to 180:"];
Print[Table[pisanotask[i], {i, 2, 180}]]
</syntaxhighlight>
{{out}}
<pre>
pisanoPrime[2, 2] = 6
pisanoPrime[3, 2] = 24
pisanoPrime[5, 2] = 100
pisanoPrime[7, 2] = 112
pisanoPrime[11, 2] = 110
pisanoPrime[13, 2] = 364
pisanoPrime[2, 1] = 3
pisanoPrime[3, 1] = 8
pisanoPrime[5, 1] = 20
pisanoPrime[7, 1] = 16
pisanoPrime[11, 1] = 10
pisanoPrime[13, 1] = 28
pisanoPrime[17, 1] = 36
pisanoPrime[19, 1] = 18
pisanoPrime[23, 1] = 48
pisanoPrime[29, 1] = 14
pisanoPrime[31, 1] = 30
pisanoPrime[37, 1] = 76
pisanoPrime[41, 1] = 40
pisanoPrime[43, 1] = 88
pisanoPrime[47, 1] = 32
pisanoPrime[53, 1] = 108
pisanoPrime[59, 1] = 58
pisanoPrime[61, 1] = 60
pisanoPrime[67, 1] = 136
pisanoPrime[71, 1] = 70
pisanoPrime[73, 1] = 148
pisanoPrime[79, 1] = 78
pisanoPrime[83, 1] = 168
pisanoPrime[89, 1] = 44
pisanoPrime[97, 1] = 196
pisanoPrime[101, 1] = 50
pisanoPrime[103, 1] = 208
pisanoPrime[107, 1] = 72
pisanoPrime[109, 1] = 108
pisanoPrime[113, 1] = 76
pisanoPrime[127, 1] = 256
pisanoPrime[131, 1] = 130
pisanoPrime[137, 1] = 276
pisanoPrime[139, 1] = 46
pisanoPrime[149, 1] = 148
pisanoPrime[151, 1] = 50
pisanoPrime[157, 1] = 316
pisanoPrime[163, 1] = 328
pisanoPrime[167, 1] = 336
pisanoPrime[173, 1] = 348
pisanoPrime[179, 1] = 178
 
Pisano[n] for n from 2 to 180:
{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}
 
Pisano[n] using pisanoPrime for n from 2 to 180:
{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}}==
Line 1,759 ⟶ 1,964:
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|PARI/GP}}==
{{trans|Mathematica/Wolfram_Language}}
<syntaxhighlight lang="PARI/GP">
\\ Initialize an associative array equivalently
pisanos = Map();
 
\\ Function to calculate the Pisano period for a given prime p
pisano(p) = {
local(lastn, n, i);
if (p < 2, return(1));
if (mapisdefined(pisanos, p),
return(mapget(pisanos, p));
);
lastn = 0; n = 1;
for (i = 1, p^2,
[lastn, n] = [n, Mod(lastn + n, p)];
if (lastn == 0 && n == 1,
mapput(pisanos, p, i);
return(i);
);
);
return(1);
}
 
\\ Function to calculate Pisano period for a prime p and a power k
pisanoprime(p, k) = {
my(i = pisano(p));
if (!isprime(p), error("p must be prime"));
p^(k-1) * i;
}
 
\\ Function to calculate Pisano period for a composite number n
pisanotask(n) = {
my(factors = factor(n));
\\print("factors=" factors);
\\apply(x -> print("x=" x), factors);
lcm( vector(#factors~, i, pisanoprime(factors[i, 1], factors[i, 2])) );
}
 
{
\\ Print Pisano periods for prime numbers up to 15 with k=2
for (i = 1, 15,
if (isprime(i),
print("pisanoPrime[" i ", 2] = " pisanoprime(i, 2))
);
);
 
\\ Print Pisano periods for prime numbers up to 180 with k=1
for (i = 1, 180,
if (isprime(i),
print("pisanoPrime[" i ", 1] = " pisanoprime(i, 1))
);
);
 
\\ Print Pisano periods for numbers 2 to 180
print("\nPisano[n] for n from 2 to 180:");
print(vector(179, i, pisano(i+1)));
 
\\ Print Pisano periods using pisanotask for numbers 2 to 180
print("\nPisano[n] using pisanoPrime for n from 2 to 180:");
print(vector(179, i, pisanotask(i+1)));
}
</syntaxhighlight>
{{out}}
<pre>
pisanoPrime[2, 2] = 6
pisanoPrime[3, 2] = 24
pisanoPrime[5, 2] = 100
pisanoPrime[7, 2] = 112
pisanoPrime[11, 2] = 110
pisanoPrime[13, 2] = 364
pisanoPrime[2, 1] = 3
pisanoPrime[3, 1] = 8
pisanoPrime[5, 1] = 20
pisanoPrime[7, 1] = 16
pisanoPrime[11, 1] = 10
pisanoPrime[13, 1] = 28
pisanoPrime[17, 1] = 36
pisanoPrime[19, 1] = 18
pisanoPrime[23, 1] = 48
pisanoPrime[29, 1] = 14
pisanoPrime[31, 1] = 30
pisanoPrime[37, 1] = 76
pisanoPrime[41, 1] = 40
pisanoPrime[43, 1] = 88
pisanoPrime[47, 1] = 32
pisanoPrime[53, 1] = 108
pisanoPrime[59, 1] = 58
pisanoPrime[61, 1] = 60
pisanoPrime[67, 1] = 136
pisanoPrime[71, 1] = 70
pisanoPrime[73, 1] = 148
pisanoPrime[79, 1] = 78
pisanoPrime[83, 1] = 168
pisanoPrime[89, 1] = 44
pisanoPrime[97, 1] = 196
pisanoPrime[101, 1] = 50
pisanoPrime[103, 1] = 208
pisanoPrime[107, 1] = 72
pisanoPrime[109, 1] = 108
pisanoPrime[113, 1] = 76
pisanoPrime[127, 1] = 256
pisanoPrime[131, 1] = 130
pisanoPrime[137, 1] = 276
pisanoPrime[139, 1] = 46
pisanoPrime[149, 1] = 148
pisanoPrime[151, 1] = 50
pisanoPrime[157, 1] = 316
pisanoPrime[163, 1] = 328
pisanoPrime[167, 1] = 336
pisanoPrime[173, 1] = 348
pisanoPrime[179, 1] = 178
 
Pisano[n] for n from 2 to 180:
[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]
 
Pisano[n] using pisanoPrime for n from 2 to 180:
[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|Perl}}==
Line 2,340 ⟶ 2,667:
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="ecmascriptwren">import "./math" for Int
import "./fmt" for Fmt
 
// Calculates the Pisano period of 'm' from first principles.
Chkas
2,033

edits

Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/354090...361479"