

A320916


Consider A010060 as a 2adic 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
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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 realvalued (or complexvalued) function it only converges for x < 1. In 2adic field it only converges for x_2 < 1 as well, but here x_2 is a different metric. For a 2adic number x, x_2 < 1 iff x is an even 2adic integer.


LINKS

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


FORMULA

a(n) = Sum_{i=0..n1} 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, n1, 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



