A099245 Numerator of relative frequency of number of ones in the binary representation of n.

0, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 3, 1, 3, 3, 1, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 5, 1, 1, 1, 2, 1, 2, 2, 5, 1, 2, 2, 5, 2, 5, 5, 1, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3

Offset

0,6

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for sequences related to binary expansion of n.

Formula

a(n) = A099246(n)*A000120(n)/A070939(n).

a(n) = A000120(n)/A099244(n) for n > 0.

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

Example

Fractions begin with 0, 1, 1/2, 1, 1/3, 2/3, 2/3, 1, 1/4, 1/2, 1/2, 3/4, ...

Mathematica

a[0]:=0; a[n_]:=Numerator[First[#]/Total[#]] & @ DigitCount[n, 2, {1, 0}]; Array[a, 100, 0] (* Amiram Eldar, Apr 05 2025 *)
a[n_]:=Numerator[Mean[IntegerDigits[n, 2]]]; Array[a, 105, 0] (* Stefano Spezia, Apr 02 2026 *)

Prog

(Haskell)
import Data.Ratio ((%), numerator)
a099245 n = numerator $ (a000120 n) % (a070939 n)
-- Reinhard Zumkeller, Oct 10 2013

Crossrefs

Cf. A000120, A007088, A070939, A099244, A099246 (denominators).

Sequence in context: A165031 A379592 A286634 * A185331 A206474 A211999

Adjacent sequences: A099242 A099243 A099244 * A099246 A099247 A099248

Keyword

nonn,frac,base

Author

Reinhard Zumkeller, Oct 08 2004

Status

approved