A099246 Denominator of relative frequency of number of ones in the binary representation of n.

1, 1, 2, 1, 3, 3, 3, 1, 4, 2, 2, 4, 2, 4, 4, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 6, 3, 3, 2, 3, 2, 2, 3, 3, 2, 2, 3, 2, 3, 3, 6, 3, 2, 2, 3, 2, 3, 3, 6, 2, 3, 3, 6, 3, 6, 6, 1, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset: 0

Author

Reinhard Zumkeller, Oct 08 2004

Keywords

• nonn
• frac
• base

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to binary expansion of n.

Crossrefs

Cf. A000120, A000225, A007088, A070939, A099244, A099245 (numerators).

Programs

Haskell

import Data.Ratio ((%), denominator)
a099246 n = denominator $ (a000120 n) % (a070939 n)
-- Reinhard Zumkeller, Oct 10 2013

Mathematica

a[n_] := Denominator[First[#]/Total[#]] & @ DigitCount[n, 2, {1, 0}]; Array[a, 100, 0] (* Amiram Eldar, Apr 05 2025 *)

Formula

a(n)*A000120(n) = A099245(n)*A070939(n).

a(n) = A070939(n)/A099244(n) for n > 0.

a(n) = 1 iff n = A000225(k).

a(n) = if n=0 then 1 else A070939(n)/GCD(A070939(n), A000120(n)).