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A351706 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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
The function d is a bijection from the nonnegative integers to the nonnegative dyadic rationals satisfying d(A000695(n)) = n for any n >= 0.
LINKS
Wikipedia, Dyadic rational
FORMULA
a(A000695(n)) = 1.
a(2^k) = A072345(k) for any k >= 0.
a(2^k-1) = A016116(k) for any k >= 0.
EXAMPLE
For n = 13:
- 13 = 2^0 + 2^2 + 2^3,
- A130472(0) = 0, A130472(2) = 1, A130472(3) = -2,
- d(13) = 2^0 + 2^1 + 2^-2 = 13/4,
- so a(13) = 4.
PROG
(PARI) a(n) = { my (d=0, k); while (n, n-=2^k=valuation(n, 2); d+=2^((-1)^k*(k+1)\2)); denominator(d) }
CROSSREFS
Sequence in context: A332381 A349195 A164516 * A016533 A122915 A327193
KEYWORD
nonn,base,frac
AUTHOR
Rémy Sigrist, Feb 16 2022
STATUS
approved

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Last modified March 29 05:16 EDT 2024. Contains 371264 sequences. (Running on oeis4.)