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 A140085 Period 8: repeat [0,1,1,2,1,2,2,3]. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1). FORMULA a(n) = (1/56)*{24*(n mod 8)-4*[(n+1) mod 8]+3*[(n+2) mod 8]-4*[(n+3) mod 8]+10*[(n+4) mod 8]-4*[(n+5) mod 8]+3*[(n+6) mod 8]-4*[(n+7) mod 8]}, with n>=0 - Paolo P. Lava, Jun 06 2008 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

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Last modified April 21 07:26 EDT 2021. Contains 343146 sequences. (Running on oeis4.)