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 A274183 #5 Jun 16 2016 13:54:44
%S A274183 0,1,0,2,1,0,3,2,1,1,0,4,3,2,2,1,1,0,5,4,3,3,2,2,1,2,1,1,0,6,5,4,4,3,
%T A274183 3,2,3,2,2,1,2,1,1,1,0,7,6,5,5,4,4,3,4,3,3,2,3,2,2,2,1,3,2,2,1,1,1,1,
%U A274183 0,8,7,6,6,5,5,4,5,4,4,3,4,3,3,3,2,4
%N A274183 Irregular triangular array having n-th row g(n) defined in Comments.
%C A274183 Let g(0) = (0) and for n > 0, define g(n) inductively as the concatenation of g(n-1) and the numbers k/2 as k ranges through the even 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 A274183 First six rows:
%e A274183 0
%e A274183 1 0
%e A274183 2 1 0
%e A274183 3 2 1 1 0
%e A274183 4 3 2 2 1 1 0
%e A274183 5 4 3 3 2 2 1 2 1 1 0
%t A274183 g[0] = {0}; z = 14; g[n_] := g[n] = Join[g[n - 1] + 1, (1/2) Select[g[n - 1], IntegerQ[#/2] &]]; Flatten[Table[g[n], {n, 0, z}]]
%Y A274183 Cf. A274184 (row lengths), A274192, A274185.
%K A274183 nonn,tabf,easy
%O A274183 0,4
%A A274183 _Clark Kimberling_, Jun 13 2016