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%I #43 Sep 23 2023 07:28:49
%S 0,0,2,6,6,22,22,22,150,406,406,406,2454,2454,10646,27030,27030,92566,
%T 92566,92566,616854,616854,2714006,6908310,6908310,6908310,40462742,
%U 107571606,107571606,376007062,376007062,376007062,2523490710,6818458006,6818458006,6818458006
%N Consider A010060 as a 2-adic number ...100110010110, then a(n) is its approximation up to 2^n.
%C This is another interpretation of A010060 as a number, in a different way as considering it as a binary number.
%C 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.
%F a(n) = Sum_{i=0..n-1} A010060(i)*2^i (empty sum yields 0 for n = 0).
%e a(1) = 0_2 = 0.
%e a(2) = 10_2 = 2.
%e a(3) = 110_2 = 6.
%e a(4) = 0110_2 = 6.
%e a(5) = 10110_2 = 22.
%e ...
%o (PARI) a(n) = sum(i=0, n-1, 2^i*(hammingweight(i)%2))
%Y Cf. A010060, A122570, A019300 (bit reversal).
%K nonn,easy
%O 0,3
%A _Jianing Song_, Oct 26 2018
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