Pell numbers: Difference between revisions

==={{header|FreeBASIC}}===

{{trans|Phix}}

 

Function isPrime(Byval ValorEval As Integer) As Boolean

i += 1

Loop

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<pre style="height:40ex;overflow:scroll;">First 20 Pell numbers:

{{trans|Wren}}

{{libheader|Go-rcu}}

 

import (

u1 = u2

}

 

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For example:

 

Pn=: (%:8) %~(1+%:2)&^ - (1-%:2)&^ NB. pell, closed form

Qn=: (1+%:2)&^ + (1-%:2)&^ NB. pell lucas, closed form

QN=: +: %&Pn ] NB. pell lucas, closed form

 

Thus:

 

0 1 2 5 12 29 70 169 408 985 2378

Pn i.11

0 2 6 14 34 82 198 478 1154 2786 6726

qn i.11

 

QN (which is defined as P_2n/P_n) doesn't get the first element of the pell lucas sequence right. We could fix this by changing the definition:

 

QN i.11

 

Continuing... the first ten rational approximations to √2 here would be:

1 1.5 1.4 1.41667 1.41379 1.41429 1.4142 1.41422 1.41421 1.41421

}.(%~ _1}. +//.@,:~) nextPell^:9(0 1x)

 

The first ten pell primes are:

 

Their indices are:

 

The NSW numbers are the sums of (non-overlapping) pairs of pell numbers, or:

1 7 41 239 1393 8119 47321 275807 1607521 9369319 54608393

 

The first ten pell based pythogorean triples would be:

3 4 5

20 21 29

803760 803761 1136689

4684659 4684660 6625109

 

=={{header|Julia}}==

 

function pellnumbers(wanted)

printrows("Twenty Newman-Shank-Williams numbers:", newmanshankwilliams(20), 17, 5)

printrows("Twenty near isosceles triangle triplets:", nearisosceles(20), 52, 2)

<pre>

Twenty Pell numbers:

 

=={{header|Mathematica}}/{{header|Wolfram Language}}==

PellNumber[0] = 0;

PellNumber[1] = 1;

{short, long, hypo}

]

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<pre>{0, 1, 2, 5, 12, 29, 70, 169, 408, 985}

=={{header|Perl}}==

{{libheader|ntheory}}

use warnings;

use feature <state say>;

my $x = sum @pell[0..$y-1];

printf "(%d, %d, %d)\n", $x, $x+1, $pell[$y]

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<pre style="height:20ex">First 20 Pell numbers:

 

=={{header|Phix}}==

<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>

<span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</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, %d, %d]\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">side</span><span style="color: #0000FF;">,</span><span style="color: #000000;">side</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">hypot</span><span style="color: #0000FF;">})</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>

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<pre>

 

=={{header|Raku}}==

my $pell-lucas = lazy 2, 2, * + * × 2 … *;

 

 

say "\nFirst $upto near isosceles right triangles:";

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<pre style="height:40ex;overflow:scroll;">First 20 Pell numbers:

 

=={{header|Scala}}==

BigInt("0") #:: BigInt("1") #::

(pellNumbers zip pellNumbers.tail).

println(pellTriple.take(10).mkString("7. Near Right-triangle Triples: \n\n", "\n", "\n"))

}

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<pre style="height:48ex;overflow:scroll;>7 Tasks

{{libheader|Wren-math}}

{{libheader|Wren-fmt}}

import "./math" for Int

import "./fmt" for Fmt

p1 = p2

i = i + 1

 

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