A294657 Largest number in the orbit of n under iteration of the map A125256: x -> smallest odd prime divisor of n^2+1.

13, 13, 17, 13, 37, 13, 13, 421, 5101, 1861, 13, 13, 197, 113, 257, 17, 18, 16381, 401, 21, 22, 23, 577, 313, 677, 27, 28, 421, 30, 31, 32, 33, 34, 613, 1297, 37, 38, 761, 1601, 421, 42, 43, 44, 1013, 421, 47, 48, 1201, 421, 1301, 52, 53, 2917, 55, 3137, 57, 58, 1515541, 60

Offset: 2

Author

M. F. Hasler, Nov 06 2017

Keywords

• nonn

Comments

The orbit (or trajectory) under A125256 appears to end in the cycle 5 -> 13 -> 5 -> etc. for any initial value n.

Links

• Ray Chandler, Table of n, a(n) for n = 2..20001

Crossrefs

Cf. A125256, A294656 (size of the orbit).

Programs

Mathematica

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 *)

PARI

A294657(n,S=[n])={while(#S<#S=setunion(S,[n=A125256(n)]),); vecmax(S)}