Pell numbers: Difference between revisions
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(211929657785303, 211929657785304, 299713796309065) (1235216565974040, 1235216565974041, 1746860020068409)
</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<lang Mathematica>ClearAll[PellNumber, PellLucasNumber]
PellNumber[0] = 0;
PellNumber[1] = 1;
PellNumber[n_] := PellNumber[n] = 2 PellNumber[n - 1] + PellNumber[n - 2]
PellLucasNumber[0] = 2;
PellLucasNumber[1] = 2;
PellLucasNumber[n_] := PellLucasNumber[n] = 2 PellLucasNumber[n - 1] + PellLucasNumber[n - 2]
pns = PellNumber /@ Range[0, 9]
plns = PellLucasNumber /@ Range[0, 9]
den = Rest@pns;
num = Rest@plns/2;
approx = num/den
N[approx]
pns = {#, PellNumber[#]} & /@ Range[0, 100];
Select[pns, Last/*PrimeQ, 10] // Grid
ClearAll[PellS]
PellS[n_] := If[n == 0, 1, PellNumber[2 n] + PellNumber[2 n + 1]]
PellS /@ Range[0, 19]
ClearAll[PythagoreanTriple]
PythagoreanTriple[n_Integer] := Module[{hypo, short, long},
hypo = PellNumber[2 n + 1];
short = Total[PellNumber /@ Range[2 n]];
long = short + 1;
{short, long, hypo}
]
PythagoreanTriple /@ Range[10]</lang>
{{out}}
<pre>{0, 1, 2, 5, 12, 29, 70, 169, 408, 985}
{2, 2, 6, 14, 34, 82, 198, 478, 1154, 2786}
{1, 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, 577/408, 1393/985}
{1., 1.5, 1.4, 1.41667, 1.41379, 1.41429, 1.4142, 1.41422, 1.41421}
2 2
3 5
5 29
11 5741
13 33461
29 44560482149
41 1746860020068409
53 68480406462161287469
59 13558774610046711780701
89 4125636888562548868221559797461449
{1, 7, 41, 239, 1393, 8119, 47321, 275807, 1607521, 9369319, 54608393, 318281039, 1855077841, 10812186007, 63018038201, 367296043199, 2140758220993, 12477253282759, 72722761475561, 423859315570607}
{{3, 4, 5}, {20, 21, 29}, {119, 120, 169}, {696, 697, 985}, {4059, 4060, 5741}, {23660, 23661, 33461}, {137903, 137904, 195025}, {803760, 803761, 1136689}, {4684659, 4684660, 6625109}, {27304196, 27304197, 38613965}}</pre>
=={{header|Perl}}==
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