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

0,3

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.

Links

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

Example

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

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}]]

Crossrefs

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

Sequence in context: A025644 A022332 A215589 * A161162 A211000 A025636

Adjacent sequences: A274182 A274183 A274184 * A274186 A274187 A274188

Keyword

nonn,tabf,easy,base

Author

Clark Kimberling, Jun 13 2016

Status

approved