This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A068967 #14 Feb 16 2025 08:32:45
%S A068967 3,12,25,30,37,51,60,65,65,100,116,260,273,761,761,825,884,1092,1476,
%T A068967 1695,1695,1752,2415,3048,3552,4045,4134,4264,5429,6357,7267,9316,
%U A068967 14027,16095,18850,21576,29925,30261,38164,40562,45982,45982,51805,51805,82000,82000
%N A068967 Numbers that define integer Heronian triangles [a(n), prime(a(n)), A068968(n)] with area A068969(n).
%H A068967 Giovanni Resta, <a href="/A068967/b068967.txt">Table of n, a(n) for n = 1..120</a>
%H A068967 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle</a>.
%e A068967 a(5) = 37: [37, A000040(37), A068968(5)] = [37,157,130], with s = (36+157+130)/2 = 162: Area^2 = s*(s-37)*(s-157)*(s-130) = 162*125*5*32 = 3240000 = 1800*1800, therefore A068969(5) = 1800.
%t A068967 area[{a_, b_, c_}] := Block[{s = (a + b + c)/2}, Sqrt[s (s-a) (s-b) (s-c)]]; zz[n_] := Block[{s, p = Prime@ n, t, z, A}, s = Solve[(n^2 - 2 n p + p^2 - z) (z - n^2 - 2 n p - p^2) == t^2 && z>0 && t>0, {t, z}, Integers]; If[s == {}, {}, z = Sort@ Select[Sqrt[z /. s], IntegerQ]]; Select[Table[{n, p, e}, {e, z}], IntegerQ[A = area[#]] && A > 0 &]]; (Join @@ Parallelize@ Array[zz, 4300])[[All, 1]] (* _Giovanni Resta_, Apr 20 2020 *)
%Y A068967 Cf. A068968, A068969, A068964.
%K A068967 nonn
%O A068967 1,1
%A A068967 _Reinhard Zumkeller_, Mar 30 2002
%E A068967 Erroneous term 2374 removed and more terms from _Giovanni Resta_, Apr 20 2020