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 A120684 #11 Sep 24 2013 00:41:42 %S A120684 3,6,7,9,12,14,18,19,21,24,27,28,29,31,35,36,38,42,43,48,49,54,56,57, %T A120684 58,59,62,63,67,70,72,73,76,79,81,84,86,87,89,93,95,96,98,101,103,105, %U A120684 108,109,112,114,116,118,124,126,127,129,131,133,134,137,140,144,145,146 %N A120684 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 3 -> 4 -> 3 -> ... %C A120684 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 C3 as the one that begin with 3. In A120685 we present C4 as the one that begin with 4. %e A120684 Oscillation between 3 and 4: 1+gpf(3)=1+3=4; 1+gpf(4)=1+2=3. %e A120684 Other value, e.g. 7: 1+gpf(7)=1+7=8; 1+gpf(8)=1+2=3 (7 belongs to C3). %e A120684 Other value, e.g. 20: 1+gpf(20)=1+5=6; 1+gpf(6)=1+3=4 (20 belongs to C4). %t A120684 f = Function[n, FactorInteger[n][[ -1, 1]] + 1]; mn = Map[(NestList[f, #, 8][[ -1]]) &, Range[2, 500]]; out = Flatten[Position[mn, 3]] + 1 %Y A120684 Cf. A072268, A006530. %K A120684 nonn %O A120684 0,1 %A A120684 _Carlos Alves_, Jun 25 2006 %E A120684 Edited by _Michel Marcus_, Feb 23 2013