Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 May 04 2019 16:17:50
%S 13,13,17,13,37,13,13,421,5101,1861,13,13,197,113,257,17,18,16381,401,
%T 21,22,23,577,313,677,27,28,421,30,31,32,33,34,613,1297,37,38,761,
%U 1601,421,42,43,44,1013,421,47,48,1201,421,1301,52,53,2917,55,3137,57,58,1515541,60
%N Largest number in the orbit of n under iteration of the map A125256: x -> smallest odd prime divisor of n^2+1.
%C The orbit (or trajectory) under A125256 appears to end in the cycle 5 -> 13 -> 5 -> etc. for any initial value n.
%H Ray Chandler, <a href="/A294657/b294657.txt">Table of n, a(n) for n = 2..20001</a>
%t 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 (PARI) A294657(n,S=[n])={while(#S<#S=setunion(S,[n=A125256(n)]),); vecmax(S)}
%Y Cf. A125256, A294656 (size of the orbit).
%K nonn
%O 2,1
%A _M. F. Hasler_, Nov 06 2017