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 A274185 #9 Jun 21 2016 11:03:30
%S A274185 0,1,2,0,3,1,4,2,1,0,5,3,2,1,0,6,4,3,2,1,2,1,0,7,5,4,3,2,3,2,1,1,0,0,
%T A274185 8,6,5,4,3,4,3,2,2,1,1,3,2,1,1,0,0,9,7,6,5,4,5,4,3,3,2,2,4,3,2,2,1,1,
%U A274185 2,1,1,0,0,1,0,0,10,8,7,6,5,6,5,4,4,3
%N A274185 Irregular triangular array having n-th row g(n) defined in Comments.
%C A274185 Let g(0) = (0) and for n > 0, define g(n) inductively to be the concatenation of g(n-1) and the numbers (k-1)/2 as k ranges through the odd numbers k in g(n-1). Every nonnegative integer appears infinitely many times. For the limiting ratio of lengths of consecutive rows, see A274192.
%e A274185 First seven rows:
%e A274185 0
%e A274185 1
%e A274185 2 0
%e A274185 3 1
%e A274185 4 2 1 0
%e A274185 5 3 2 1 0
%e A274185 6 4 3 2 1 2 1 0
%t A274185 g[0] = {0}; z = 14; g[n_] := g[n] = Join[g[n - 1] + 1, (1/2) (Select[g[n - 1], IntegerQ[(# - 1)/2] &] - 1)]; Flatten[Table[g[n], {n, 0, z}]]
%Y A274185 Cf. A274142 (row lengths), A274192, A274183.
%K A274185 nonn,tabf,easy,base
%O A274185 0,3
%A A274185 _Clark Kimberling_, Jun 13 2016