A294657 - OEIS

A294657

Largest number in the orbit of n under iteration of the map A125256: x -> smallest odd prime divisor of n^2+1.

%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