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

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

Offset: 1

Author

Lekraj Beedassy, Jul 18 2002

Keywords

• nonn

Comments

Such a triangle has middle side 2*x'.

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A072330, A086909, 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, 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]]]]];
a /@ Range[terms] (* Jean-François Alcover, Mar 07 2020 *)

Formula

a(n) = x'*y'/2, where (x', y') is the fundamental solution to x^2 - 3*y^2 = d^2, where d=A072330(n).

Extensions

Edited, corrected and extended by Ray Chandler, Jul 03 2004