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 A139124 #16 Jul 01 2025 09:03:13
%S A139124 1,1,2,1,2,2,3,1,3,3,3,3,4,1,5,3,4,1,2,6,3,5,1,2,2,7,4,6,1,2,2,3,7,6,
%T A139124 7,3,3,2,3,8,8,8,3,3,3,2,3,11,9,8,1,0,1,4,3,3,2,3,15,10,8,1,0,0,0,1,1,
%U A139124 1,5,3,3,2,4,18,11,10,1,0,0,1,0,0,0,2,2,1,5,3,3,3,5,20,12,14
%N A139124 Starting from 1, at any step count the appearances of k, where k ranges from the highest number to 1.
%e A139124 Start from 1. There is just one 1. So the sequence becames 1,1. Then count two 1s.
%e A139124 So we have 1,1,2. Then one 2 and two 1 -> 1,1,2,1,2. Then two 2 and three 1 -> 1,1,2,1,2,2,3. Then one 3, three 2, three 1 -> 1,1,2,1,2,2,3,1,3,3. Then three 3, three 2 and four 1 -> 1,1,2,1,2,2,3,1,3,3,3,3,4. And so on.
%t A139124 s={1};Do[si={};Do[j=Max[s]-i+1;AppendTo[si,Count[s,j]],{i,Max[s]}];s=AppendTo[s,si]//Flatten,{n,15}];s (* _James C. McMahon_, Jun 29 2025 *)
%Y A139124 Cf. A030717, A333867.
%K A139124 easy,nonn
%O A139124 0,3
%A A139124 _Paolo P. Lava_ and _Giorgio Balzarotti_, Apr 15 2008
%E A139124 a(87)-a(89) inserted by _James C. McMahon_, Jun 29 2025