A370303 a(n) = A370302(n)-A000523(n)-3.

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, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2

Offset: 1

Author

Pontus von Brömssen, Feb 14 2024

Keywords

• nonn

Comments

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.)

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..1023

Crossrefs

Cf. A000523, A370302.

Formula

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