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A320916 Consider A010060 as a 2-adic number ...100110010110, then a(n) is its approximation up to 2^n. 0
0, 0, 2, 6, 6, 22, 22, 22, 150, 406, 406, 406, 2454, 2454, 10646, 27030, 27030, 92566, 92566, 92566, 616854, 616854, 2714006, 6908310, 6908310, 6908310, 40462742, 107571606, 107571606, 376007062, 376007062, 376007062, 2523490710, 6818458006, 6818458006, 6818458006 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This is another interpretation of A010060 as a number, in a different way as considering it as a binary number.

Consider the g.f. of A010060. As a real-valued (or complex-valued) function it only converges for |x| < 1. In 2-adic field it only converges for |x|_2 < 1 as well, but here |x|_2 is a different metric. For a 2-adic number x, |x|_2 < 1 iff x is an even 2-adic integer.

LINKS

Table of n, a(n) for n=0..35.

FORMULA

a(n) = Sum_{i=0..n-1} A010060(i)*2^i (empty sum yields 0 for n = 0).

EXAMPLE

a(1) =     0_2 =  0.

a(2) =    10_2 =  2.

a(3) =   110_2 =  6.

a(4) =  0110_2 =  6.

a(5) = 10110_2 = 22.

...

PROG

(PARI) a(n) = sum(i=0, n-1, 2^i*(hammingweight(i)%2))

CROSSREFS

Cf. A010060.

Sequence in context: A083774 A081518 A258702 * A119551 A100634 A242527

Adjacent sequences:  A320913 A320914 A320915 * A320917 A320918 A320919

KEYWORD

nonn

AUTHOR

Jianing Song, Oct 26 2018

STATUS

approved

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Last modified November 14 17:24 EST 2019. Contains 329126 sequences. (Running on oeis4.)