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%I #15 Oct 11 2021 12:00:38
%S 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,
%T 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,
%U 9,6,7,3,10,7,8,4,9,5,6,2,11,8,9,5,10,6
%N Length of longest sequence of directed edges in the graph G (see Comments) that starts at node n.
%C 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.
%C Thus from vertex 12 = 1100_2 there are outgoing edges to vertex 11 = 12 - 1 and to vertex 10 = 12 - 2.
%C Then a(n) is the length of the longest sequence of edges starting at vertex n.
%C If we replace "0" by "1" in the definition, the analogous sequence is A000120. - _Andrey Zabolotskiy_, Oct 10 2021.
%H Rémy Sigrist, <a href="/A347696/b347696.txt">Table of n, a(n) for n = 0..8191</a>
%H Rémy Sigrist, <a href="/A347696/a347696.txt">C program for A347696</a>
%H Ravi Vakil, <a href="https://doi.org/10.1016/S0012-365X(98)00383-5">On the Steenrod length of real projective spaces: finding longest chains in certain directed graphs</a>, Discrete Mathematics 204 (1999) 415-425.
%o (C) See Links section.
%Y Cf. A000120, A347697.
%K nonn
%O 0,5
%A _N. J. A. Sloane_, Oct 10 2021
%E More terms from _Rémy Sigrist_, Oct 11 2021
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