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 A294657 #11 May 04 2019 16:17:50
%S A294657 13,13,17,13,37,13,13,421,5101,1861,13,13,197,113,257,17,18,16381,401,
%T A294657 21,22,23,577,313,677,27,28,421,30,31,32,33,34,613,1297,37,38,761,
%U A294657 1601,421,42,43,44,1013,421,47,48,1201,421,1301,52,53,2917,55,3137,57,58,1515541,60
%N A294657 Largest number in the orbit of n under iteration of the map A125256: x -> smallest odd prime divisor of n^2+1.
%C A294657 The orbit (or trajectory) under A125256 appears to end in the cycle 5 -> 13 -> 5 -> etc. for any initial value n.
%H A294657 Ray Chandler, <a href="/A294657/b294657.txt">Table of n, a(n) for n = 2..20001</a>
%t A294657 Table[Max[NestWhileList[SelectFirst[FactorInteger[#^2+1][[All,1]], OddQ]&, n,#!=13&]],{n,2,60}] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 04 2019 *)
%o A294657 (PARI) A294657(n,S=[n])={while(#S<#S=setunion(S,[n=A125256(n)]),); vecmax(S)}
%Y A294657 Cf. A125256, A294656 (size of the orbit).
%K A294657 nonn
%O A294657 2,1
%A A294657 _M. F. Hasler_, Nov 06 2017