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

0,6

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.

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

Example

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.

Prog

(Fortran) See Sloane link.

Crossrefs

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

Cf. A140137, A140138, A140200-A140206.

Sequence in context: A117355 A319571 A086966 * A345927 A065359 A087372

Adjacent sequences: A140077 A140078 A140079 * A140081 A140082 A140083

Keyword

nonn

Author

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

Status

approved