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
Paolo Xausa, Table of n, a(n) for n = 0..1000
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
KEYWORD
nonn,easy
AUTHOR
Jianing Song, Oct 26 2018
STATUS
approved