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