A274183 Irregular triangular array having n-th row g(n) defined in Comments.

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

Offset

0,4

Comments

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.

Links

Table of n, a(n) for n=0..85.

Example

First six rows:
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

Mathematica

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}]]

Crossrefs

Cf. A274184 (row lengths), A274192, A274185.

Sequence in context: A365004 A096652 A322133 * A212278 A244215 A389733

Adjacent sequences: A274180 A274181 A274182 * A274184 A274185 A274186

Keyword

nonn,tabf,easy

Author

Clark Kimberling, Jun 13 2016

Status

approved