A140085 Period 8: repeat [0,1,1,2,1,2,2,3].

0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1

Offset

0,4

Comments

Also fix e = 8; then 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.

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.

Links

Table of n, a(n) for n=0..98.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1).

Formula

a(n) = 3/2 -cos(Pi*n/4)/4 -(1+sqrt(2))*sin(Pi*n/4)/4 -cos(Pi*n/2)/2 -sin(Pi*n/2)/2 -cos(3*Pi*n/4)/4 +(1-sqrt(2))*sin(3*Pi*n/4)/4 -(-1)^n/2. - R. J. Mathar, Oct 08 2011

a(n) = a(n-8). G.f.: -x*(3*x^6+2*x^5+2*x^4+x^3+2*x^2+x+1) / ((x-1)*(x+1)*(x^2+1)*(x^4+1)). - Colin Barker, Jul 26 2013

Prog

See link in A140080 for Fortran program.

Crossrefs

Sequence in context: A279861 A321431 A338984 * A071445 A144081 A278838

Adjacent sequences: A140082 A140083 A140084 * A140086 A140087 A140088

Keyword

nonn,easy

Author

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

Status

approved