34 lines
855 B
Plaintext
34 lines
855 B
Plaintext
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]
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