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 A120685 #12 Jan 03 2024 17:08:47 %S A120685 2,4,5,8,10,11,13,15,16,17,20,22,23,25,26,30,32,33,34,37,39,40,41,44, %T A120685 45,46,47,50,51,52,53,55,60,61,64,65,66,68,69,71,74,75,77,78,80,82,83, %U A120685 85,88,90,91,92,94,97,99,100,102,104,106,107,110,111,113,115,117,119,120 %N A120685 Integers m such that the sequence defined by f(0)=m and f(n+1)=1+gpf(f(n)), with gpf(n) being the greatest prime factor of n (A006530), ends up in the repetitive cycle 4 -> 3 -> 4 -> ... %C A120685 Let f(0)=m; f(n+1)=1+gpf(f(n)), where gpf(n) is the greatest prime factor of n (A006530). For any m, for sufficiently large n the sequence f(n) oscillates between 3 and 4. Given a sufficiently large n, this allows us to divide integers in two classes: C3 (m such that the sequence f(n) enters the cycle 3, 4, 3, ...) and C4 (m such that the sequence f(n) enters the cycle 4, 3, 4, ...). We present here C4 as the one that begin with 4. In A120684 we present C3 as the one that begin with 3. %e A120685 Oscillation between 3 and 4: 1+gpf(3)=1+3=4; 1+gpf(4)=1+2=3. %e A120685 Other value, e.g. 7: 1+gpf(7)=1+7=8; 1+gpf(8)=1+2=3 (7 belongs to C3). %e A120685 Other value, e.g. 20: 1+gpf(20)=1+5=6; 1+gpf(6)=1+3=4 (20 belongs to C4). %t A120685 f = Function[n, FactorInteger[n][[ -1, 1]] + 1]; mn = Map[(NestList[f, #, 8][[ -1]]) &, Range[2, 500]]; out = Flatten[Position[mn, 4]] + 1 %Y A120685 Cf. A120684, A072268, A006530. %K A120685 nonn %O A120685 0,1 %A A120685 _Carlos Alves_, Jun 25 2006 %E A120685 Edited by _Michel Marcus_, Feb 25 2013