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A089020
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First value y satisfying x^2 - 3*y^2 = d^2, where d=A072330(n).
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8
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1, 4, 3, 7, 5, 8, 11, 16, 20, 7, 13, 20, 12, 44, 9, 51, 17, 52, 57, 55, 19, 11, 16, 28, 72, 91, 36, 65, 69, 13, 23, 68, 20, 25, 105, 15, 88, 76, 44, 120, 145, 40, 87, 119, 29, 85, 24, 17, 155, 132, 93, 31, 44, 104, 52, 92, 95, 19, 140, 200, 28, 105, 231, 35, 100, 185, 105, 120
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OFFSET
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1,2
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LINKS
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MATHEMATICA
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terms = 1000;
nmax = 12 terms;
okQ[n_] := AllTrue[FactorInteger[n][[All, 1]], MatchQ[Mod[#, 12], 1|11]&];
A072330 = Select[Range[nmax], okQ];
a[n_] := Module[{a, b, c, d, p}, d = If[n <= Length[A072330], A072330[[n]], Print["nmax = ", nmax, " insufficient"]; Exit[]]; If[n == 1, 1, For[b = 2 d, True, b++, a = b - d; c = b + d; p = (a + b + c)/2; If[IntegerQ[p] && IntegerQ[Sqrt[p (p - a) (p - b) (p - c)]] && GCD[a, b, c] == 1, Return[ Sqrt[b^2 - 4 d^2]/(2 Sqrt[3])]]]]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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