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A072360
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One-sixth the area of the smallest primitive d-arithmetic triangle, where d=A072330(n).
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8
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1, 26, 21, 91, 95, 196, 341, 536, 790, 259, 559, 1030, 654, 2926, 549, 4029, 1241, 4706, 5529, 5335, 1729, 1001, 1544, 2786, 9324, 12649, 4446, 8645, 9591, 1651, 3059, 10234, 3010, 3925, 19005, 2535, 16676, 14174, 8074, 25620, 33205, 8060
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OFFSET
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1,2
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COMMENTS
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Such a triangle has middle side 2*x'.
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LINKS
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FORMULA
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a(n) = x'*y'/2, where (x', y') is the fundamental solution to x^2 - 3*y^2 = d^2, where d=A072330(n).
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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, area}, 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[area = Sqrt[p (p - a) (p - b) (p - c)]] && GCD[a, b, c] == 1, Return[area/6]]]]];
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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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