A086909 Middle side of the first primitive d-arithmetic triangle, where d=A072330(n).

4, 26, 28, 52, 76, 98, 124, 134, 158, 148, 172, 206, 218, 266, 244, 316, 292, 362, 388, 388, 364, 364, 386, 398, 518, 556, 494, 532, 556, 508, 532, 602, 602, 628, 724, 676, 758, 746, 734, 854, 916, 806, 868, 916, 844, 892, 866, 868, 1036, 1022, 988, 964, 974

Offset: 1

Author

Lekraj Beedassy, Sep 19 2003

Keywords

• nonn

References

• J. A. MacDougall, "Heron Triangles With Sides In Arithmetic Progression", Journal of Recreational Mathematics 31(3) 2002-2003, pp. 192-194.

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..1000
• J. A. MacDougall, Heron Triangles With Sides In Arithmetic Progression, ResearchGate, 2005.

Crossrefs

Cf. A072330, A072360, A089019, A089020, A096672, A096673, A096674.

Programs

Mathematica

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, 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]]]]];
a /@ Range[terms] (* Jean-François Alcover, Mar 06 2020 *)

Extensions

Extended by Ray Chandler, Jul 03 2004