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 A358210 #16 Dec 21 2022 21:59:03
%S A358210 6,15,34,353,175234,9045146753,121609715057619333634,
%T A358210 4138643330264389621194448797227488932353,
%U A358210 27728719906622802548355602700962556264398170527494726660553210068191276023007234
%N A358210 Congruent number sequence starting from the Pythagorean triple (3,4,5).
%H A358210 G. Jacob Martens, <a href="https://arxiv.org/abs/2112.09553">Rational right triangles and the Congruent Number Problem</a>, arXiv:2112.09553 [math.GM], 2021, see section 8 The unseen recurrence, equations (79,80).
%e A358210 Starting with the triple (3,4,5) and choosing the b side we obtain by the recurrence the right triangles: (15/2, 4, 17/2), (136/15, 15/2, 353/30), (5295/136, 272/15, 87617/2040), (47663648/79425, 79425/136, 9045146753/10801800), ...
%e A358210 So a(4) = (5295/136) * (272/15) / 2 = 353.
%t A358210 nxt[{n_, p_, q_}] := Module[{n1 = Sqrt[p^4 + 4 n^2 q^4], p1 = p Sqrt[p^4 + 4 n^2 q^4], q1 = q^2 n},
%t A358210 a = p1/q1; b = 2 n1 q1/p1; c = Sqrt[p1^4 + 4 n1^2 q1^4]/(p1 q1);
%t A358210 Return [{ a b/2, Numerator[b], Denominator[b]}];]
%t A358210 l = NestList[nxt, {6, 3, 1}, 8] ;
%t A358210 l[[All, 1]]
%Y A358210 Cf. A081465 (numerators of hypotenuses).
%K A358210 nonn
%O A358210 1,1
%A A358210 _Gerry Martens_, Nov 04 2022