The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A135993

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A135993

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

#19 by Alois P. Heinz at Thu May 14 22:49:29 EDT 2020

STATUS

proposed

approved

#18 by Petros Hadjicostas at Thu May 14 10:36:10 EDT 2020

STATUS

editing

proposed

#17 by Petros Hadjicostas at Thu May 14 10:35:31 EDT 2020

NAME

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

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.

STATUS

proposed

editing

Discussion

Thu May 14

10:36

Petros Hadjicostas: Yes, you are right, even though I prefer the other way.

#16 by Petros Hadjicostas at Thu May 14 10:25:52 EDT 2020

STATUS

editing

proposed

Discussion

Thu May 14

10:31

Michel Marcus: looking at the stylesheet I wonder if the 3 (mod 2) should rather be mod 2 (without parentheses)

#15 by Petros Hadjicostas at Thu May 14 10:25:46 EDT 2020

CROSSREFS

Cf. A007953, A010060, A135941.

STATUS

proposed

editing

#14 by Petros Hadjicostas at Thu May 14 10:25:07 EDT 2020

STATUS

editing

proposed

#13 by Petros Hadjicostas at Thu May 14 10:25:01 EDT 2020

CROSSREFS

Cf. A010060, A007953, A010060.

#12 by Petros Hadjicostas at Thu May 14 10:24:12 EDT 2020

NAME

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

LINKS

J.-P. Allouche, J. Shallit and J. Sondow, <a href="http://dx.doi.org/10.1016/j.jnt.2006.06.001">Summation of series defined by counting blocks of digits</a>, J. Number Theory 123 (2007) , 133-143.

J. Jonathan Sondow and P. Petros Hadjicostas, <a href="http://arxiv.org/abs/math/0610499">The Generalized-Euler-Constant Function (z) and a Generalization of Somos's Quadratic Recurrence Constant</a>, arXiv:math/0610499 [math.CA], 2006.

J. Jonathan Sondow and P. Petros Hadjicostas, <a href="http://dx.doi.org/10.1016/j.jmaa.2006.09.081">The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant</a>, 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.

STATUS

approved

editing

#11 by Bruno Berselli at Thu Feb 04 12:25:33 EST 2016

STATUS

proposed

approved

#10 by Michel Marcus at Thu Feb 04 11:44:37 EST 2016

STATUS

editing

proposed