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A320916
Consider A010060 as a 2-adic number ...100110010110, then a(n) is its approximation up to 2^n.
2
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
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.
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.
...
MATHEMATICA
With[{nmax = 50}, Table[FromDigits[#[[-n;; ]], 2], {n, 0, nmax}] & [ThueMorse[Range[nmax, 0, -1]]]] (* or *)
A320916[n_] := FromDigits[ThueMorse[Range[n-1, 0, -1]], 2]; Array[A320916, 51, 0] (* Paolo Xausa, Oct 18 2024 *)
PROG
(PARI) a(n) = sum(i=0, n-1, 2^i*(hammingweight(i)%2))
CROSSREFS
Cf. A010060, A122570, A019300 (bit reversal).
Sequence in context: A367767 A368001 A258702 * A119551 A100634 A242527
KEYWORD
nonn,easy
AUTHOR
Jianing Song, Oct 26 2018
STATUS
approved