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%I #13 Mar 06 2020 11:41:35
%S 4,26,28,52,76,98,124,134,158,148,172,206,218,266,244,316,292,362,388,
%T 388,364,364,386,398,518,556,494,532,556,508,532,602,602,628,724,676,
%U 758,746,734,854,916,806,868,916,844,892,866,868,1036,1022,988,964,974
%N Middle side of the first primitive d-arithmetic triangle, where d=A072330(n).
%D J. A. MacDougall, "Heron Triangles With Sides In Arithmetic Progression", Journal of Recreational Mathematics 31(3) 2002-2003, pp. 192-194.
%H Jean-François Alcover, <a href="/A086909/b086909.txt">Table of n, a(n) for n = 1..1000</a>
%H J. A. MacDougall, <a href="https://www.researchgate.net/publication/242732258_Heron_Triangles_With_Sides_in_Arithmetic_Progression">Heron Triangles With Sides In Arithmetic Progression</a>, ResearchGate, 2005.
%t terms = 1000;
%t nmax = 12 terms;
%t okQ[n_] := AllTrue[FactorInteger[n][[All, 1]], MatchQ[Mod[#, 12], 1|11]&];
%t A072330 = Select[Range[nmax], okQ];
%t a[n_] := Module[{a, b, c, d, p}, d = If[n <= Length[A072330], A072330[[n]], Print["nmax = ", nmax, " insufficient"]; Exit[]]; If[n==1, 4, For[b = 2d, 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[b]]]]];
%t a /@ Range[terms] (* _Jean-François Alcover_, Mar 06 2020 *)
%Y Cf. A072330, A072360, A089019, A089020, A096672, A096673, A096674.
%K nonn
%O 1,1
%A _Lekraj Beedassy_, Sep 19 2003
%E Extended by _Ray Chandler_, Jul 03 2004
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