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.

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

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

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Wikipedia, Dyadic rational

Index entries for sequences related to binary expansion of n

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

Cf. A000695, A016116, A072345, A351705, A351785, A351786.

Sequence in context: A332381 A349195 A164516 * A016533 A122915 A327193

Adjacent sequences: A351703 A351704 A351705 * A351707 A351708 A351709

Keyword

nonn,base,frac

Author

Rémy Sigrist, Feb 16 2022

Status

approved