A274185 Irregular triangular array having n-th row g(n) defined in Comments.

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, 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, 2, 1, 1, 0, 0, 1, 0, 0, 10, 8, 7, 6, 5, 6, 5, 4, 4, 3

Offset: 0

Author

Clark Kimberling, Jun 13 2016

Keywords

• nonn
• tabf
• easy
• base

Comments

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.

Examples

			First seven rows:
0
1
2   0
3   1
4   2   1   0
5   3   2   1   0
6   4   3   2   1   2   1   0
		

Crossrefs

Cf. A274142 (row lengths), A274192, A274183.

Programs

Mathematica

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}]]