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A072360 One-sixth the area of the smallest primitive d-arithmetic triangle, where d=A072330(n).

%I A072360 #13 Mar 07 2020 05:05:35
%S A072360 1,26,21,91,95,196,341,536,790,259,559,1030,654,2926,549,4029,1241,
%T A072360 4706,5529,5335,1729,1001,1544,2786,9324,12649,4446,8645,9591,1651,
%U A072360 3059,10234,3010,3925,19005,2535,16676,14174,8074,25620,33205,8060
%N A072360 One-sixth the area of the smallest primitive d-arithmetic triangle, where d=A072330(n).
%C A072360 Such a triangle has middle side 2*x'.
%H A072360 Jean-François Alcover, <a href="/A072360/b072360.txt">Table of n, a(n) for n = 1..1000</a>
%F A072360 a(n) = x'*y'/2, where (x', y') is the fundamental solution to x^2 - 3*y^2 = d^2, where d=A072330(n).
%t A072360 terms = 1000;
%t A072360 nmax = 12 terms;
%t A072360 okQ[n_] := AllTrue[FactorInteger[n][[All, 1]], MatchQ[Mod[#, 12], 1|11]&];
%t A072360 A072330 = Select[Range[nmax], okQ];
%t A072360 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]]]]];
%t A072360 a /@ Range[terms] (* _Jean-François Alcover_, Mar 07 2020 *)
%Y A072360 Cf. A072330, A086909, A089019, A089020, A096672, A096673, A096674.
%K A072360 nonn
%O A072360 1,2
%A A072360 _Lekraj Beedassy_, Jul 18 2002
%E A072360 Edited, corrected and extended by _Ray Chandler_, Jul 03 2004