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 A115624 #7 Jun 13 2020 00:49:24
%S A115624 0,1,2,1,3,2,1,3,2,4,2,1,3,3,4,4,4,2,1,3,3,4,2,3,4,2,3,4,2,1,3,3,4,3,
%T A115624 3,4,4,4,5,4,4,4,4,2,1,3,3,4,3,3,4,2,3,4,5,4,4,3,5,5,4,2,4,4,4,2,1,3,
%U A115624 3,4,3,3,4,3,3,4,5,4,4,3,5,5,5,4,2,5,4,4,5,5,4,4,3,4,4,2
%N A115624 Number of iterations of signature function required to get to [1] from partitions in Mathematica order.
%C A115624 The signature function takes a partition to the partition consisting of its repetition factors.
%H A115624 Robert Price, <a href="/A115624/b115624.txt">Table of n, a(n) for n = 1..9295</a> (first 25 rows).
%e A115624 Partition 5 in Mathematica order is [2,1]. Applying the signature function to this repeatedly gives [2,1] -> [1^2] -> [2] -> [1], so a(5)=3.
%t A115624 sig[x_] := Length@NestWhileList[Last@Transpose@Tally@# &, x, # != {1} &, 1] - 1;
%t A115624 Table[sig /@ IntegerPartitions[n], {n, 8}] // Flatten (* _Robert Price_, Jun 12 2020 *)
%Y A115624 Cf. A115621, A113787, Sequence of first partitions with a(m)=n is A012257, with initial rows {1} and {2} in prepended. See A080577 for Mathematica partition order.
%K A115624 easy,nonn
%O A115624 1,3
%A A115624 _Franklin T. Adams-Watters_, Jan 25 2006