login
A347696
Length of longest sequence of directed edges in the graph G (see Comments) that starts at node n.
2
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
0,5
COMMENTS
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.
PROG
(C) See Links section.
CROSSREFS
Sequence in context: A119387 A335905 A055941 * A365385 A366788 A290537
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 10 2021
EXTENSIONS
More terms from Rémy Sigrist, Oct 11 2021
STATUS
approved