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 A068968 #14 Feb 16 2025 08:32:45
%S A068968 4,35,120,113,130,260,319,252,372,609,595,1905,2020,5712,5790,6148,
%T A068968 7735,8789,13651,14126,14576,14725,19856,25907,29603,36366,41425,
%U A068968 44325,53628,66164,67830,103525,141044,164396,229121,223805,367336,366860,446405,447855,538135
%N A068968 Sides of integer Heronian triangles [A068967(n), prime(A068967(n)), a(n)] with area A068969(n).
%H A068968 Giovanni Resta, <a href="/A068968/b068968.txt">Table of n, a(n) for n = 1..120</a>
%H A068968 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle</a>.
%e A068968 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 A068968 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, 3]] (* _Giovanni Resta_, Apr 20 2020 *)
%K A068968 nonn
%O A068968 1,1
%A A068968 _Reinhard Zumkeller_, Mar 30 2002
%E A068968 Erroneous term 21254 removed and more terms from _Giovanni Resta_, Apr 20 2020