A140080 Fix e = 3; a(n) = minimal Hamming distance between the binary representation of n and the binary representation of any multiple ke (0 <= k <= n/e) which is a child of n.

0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 2, 1, 0, 1, 1, 0, 1, 2, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 2, 1, 0, 1, 1, 0, 2, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1

Offset: 0

Author

Nadia Heninger and N. J. A. Sloane, Jun 03 2008

Keywords

• nonn

Comments

A number m is a child of n if the binary representation of n has a 1 in every position where the binary representation of m has a 1.

In other words, this tells us how closely (in Hamming weight) we can approximate n "from below" by a multiple of e.

Examples

			If n = 14 = 1110_2, take k=2, ke = 6 = 110_2, which is Hamming distance 1 from n. This is the best we can do, so a(14) = 1.
		

Links

• Nadia Heninger and N. J. A. Sloane, Table of n, a(n) for n = 0..5000
• N. J. A. Sloane, Fortran program for this and related sequences

Crossrefs

For e=2 and 4 through 9 see A000035 and A140081 through A140086.

Cf. A140137, A140138, A140200-A140206.

Programs

Fortran

See Sloane link.