A347697 -id:A347697 - cp's OEIS frontend

A347696 Length of longest sequence of directed edges in the graph G (see Comments) that starts at node n.

0, 0, 1, 0, 2, 1, 2, 0, 3, 2, 3, 1, 4, 2, 3, 0, 5, 3, 4, 2, 5, 3, 4, 1, 6, 4, 5, 2, 6, 3, 4, 0, 7, 5, 6, 3, 7, 4, 5, 2, 8, 5, 6, 3, 7, 4, 5, 1, 9, 6, 7, 4, 8, 5, 6, 2, 9, 6, 7, 3, 8, 4, 5, 0, 10, 7, 8, 5, 9, 6, 7, 3, 10, 7, 8, 4, 9, 5, 6, 2, 11, 8, 9, 5, 10, 6

Offset: 0

N. J. A. Sloane, Oct 10 2021

nonn

Let G be the directed graph with vertices labeled by the nonnegative integers and with an edge out of vertex n for each 0 in the binary representation of n (excluding leading zeros). If the 2^s term in n is 0, then the corresponding edge goes from vertex n to vertex n - 2^s.
Thus from vertex 12 = 1100_2 there are outgoing edges to vertex 11 = 12 - 1 and to vertex 10 = 12 - 2.
Then a(n) is the length of the longest sequence of edges starting at vertex n.
If we replace "0" by "1" in the definition, the analogous sequence is A000120. - Andrey Zabolotskiy, Oct 10 2021.

Rémy Sigrist, Table of n, a(n) for n = 0..8191
Rémy Sigrist, C program for A347696
Ravi Vakil, On the Steenrod length of real projective spaces: finding longest chains in certain directed graphs, Discrete Mathematics 204 (1999) 415-425.

Cf. A000120, A347697.

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A347696 Length of longest sequence of directed edges in the graph G (see Comments) that starts at node n.

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