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a(n) = A370302(n)-A000523(n)-3.
2

%I #6 Feb 14 2024 20:16:08

%S 0,0,1,0,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,0,1,1,

%T 1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,0,1,1,1,1,

%U 1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,2

%N a(n) = A370302(n)-A000523(n)-3.

%C Consider a graph with the least possible number of vertices, containing an induced cycle of length k+3 for each k such that 2^k is a term in the binary expansion of n (cf. A370302). a(n) is the number of vertices in this graph in excess of the length of the longest required induced cycle (A000523(n)+3). (A370302(n) is the least total number of vertices.)

%H Pontus von Brömssen, <a href="/A370303/b370303.txt">Table of n, a(n) for n = 1..1023</a>

%F a(n) = 0 if and only if n is a power of 2.

%Y Cf. A000523, A370302.

%K nonn

%O 1,29

%A _Pontus von Brömssen_, Feb 14 2024