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A351706
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For any nonnegative number n with binary expansion Sum_{k >= 0} b_k * 2^k, a(n) is the denominator of d(n) = Sum_{k >= 0} b_k * 2^A130472(k). See A351705 for the numerators.
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4
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1, 1, 2, 2, 1, 1, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 2, 2, 1, 1, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 2, 2, 1, 1, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 2, 2, 1, 1, 2
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OFFSET
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0,3
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COMMENTS
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The function d is a bijection from the nonnegative integers to the nonnegative dyadic rationals satisfying d(A000695(n)) = n for any n >= 0.
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LINKS
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FORMULA
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a(2^k) = A072345(k) for any k >= 0.
a(2^k-1) = A016116(k) for any k >= 0.
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EXAMPLE
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For n = 13:
- 13 = 2^0 + 2^2 + 2^3,
- d(13) = 2^0 + 2^1 + 2^-2 = 13/4,
- so a(13) = 4.
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PROG
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(PARI) a(n) = { my (d=0, k); while (n, n-=2^k=valuation(n, 2); d+=2^((-1)^k*(k+1)\2)); denominator(d) }
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CROSSREFS
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KEYWORD
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nonn,base,frac
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AUTHOR
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STATUS
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approved
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