A135993 - OEIS

A135993

a(0) = 0; a(n) = (floor(n/S2(n))) mod 2 for n >= 1, where S2(n) is the binary weight of n.

0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..70.

J.-P. Allouche, J. Shallit and J. Sondow, Summation of Series Defined by Counting Blocks of Digits, arXiv:math/0512399 [math.NT], 2005-2006.

J.-P. Allouche, J. Shallit and J. Sondow, Summation of series defined by counting blocks of digits, J. Number Theory 123 (2007), 133-143.

Jonathan Sondow and Petros Hadjicostas, The Generalized-Euler-Constant Function (z) and a Generalization of Somos's Quadratic Recurrence Constant, arXiv:math/0610499 [math.CA], 2006.

Jonathan Sondow and Petros Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant, J. Math. Anal. Appl. 332 (2007), 292-314.

FORMULA

a(n) = A135941(n) mod 2 for n > 0. - Michel Marcus, Feb 04 2016

EXAMPLE

a(17) = floor(17/2) mod 2 = 0.

a(18) = floor(18/2) mod 2 = 1.

PROG

(PARI) a(n) = if (n==0, 0, n\hammingweight(n) % 2); \\ Michel Marcus, Feb 04 2016

CROSSREFS

Cf. A007953, A010060, A135941.

Sequence in context: A101309 A141474 A073424 * A334414 A285966 A215530

Adjacent sequences: A135990 A135991 A135992 * A135994 A135995 A135996

KEYWORD

easy,nonn

AUTHOR

Ctibor O. Zizka, Mar 03 2008

EXTENSIONS

Converted references into links - R. J. Mathar, Oct 30 2009

STATUS

approved