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 A225643 #15 Mar 13 2018 04:16:35
%S A225643 0,0,0,1,1,2,2,2,2,3,3,4,4,5,4,4,4,5,4,6,5,6,5,6,6,6,6,7,7,7,8,8,8,9,
%T A225643 8,9,8,8,9,9,9,9,9,10,11,10,10,11,11,10,10,12,11,11,11,11,11,11,11,11,
%U A225643 12,12,12,12,11,13,12,12,12,12,12,12,13,13,14,14
%N A225643 Number of steps to reach a fixed point (A003418(n)), when starting from partition {n} of n and continuing with the process described in A225642.
%C A225643 a(0)=0, as its only partition is an empty partition {}, and by convention lcm()=1, thus it takes no steps to reach from 1 to A003418(0)=1.
%C A225643 The records occur at positions 0, 3, 5, 9, 11, 13, 19, 27, 30, 33, 43, 44, 51, 65, 74, 82, ... and they seem to occur in order, i.e., as A001477. Thus the record-positions probably also give the left inverse function for this sequence. It also seems that each integer occurs only finite times in this sequence, so there should be a right inverse function as well.
%F A225643 a(n) = A225644(n) - 1.
%o A225643 (Scheme) (define (A225643 n) (-1+ (A225644 n)))
%Y A225643 Cf. A225644, A225633, A225639, A226055, A226056.
%K A225643 nonn
%O A225643 0,6
%A A225643 _Antti Karttunen_, May 15 2013