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A320916
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Consider A010060 as a 2-adic number ...100110010110, then a(n) is its approximation up to 2^n.
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1
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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
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0,3
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n) = Sum_{i=0..n-1} A010060(i)*2^i (empty sum yields 0 for n = 0).
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EXAMPLE
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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.
...
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PROG
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(PARI) a(n) = sum(i=0, n-1, 2^i*(hammingweight(i)%2))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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