A033095 Number of 1's when n is written in base b for 2<=b<=n+1.

1, 1, 3, 4, 6, 6, 9, 6, 10, 10, 12, 11, 16, 13, 15, 14, 16, 13, 18, 15, 21, 20, 21, 16, 24, 20, 23, 23, 26, 25, 32, 22, 26, 25, 25, 28, 34, 28, 32, 30, 35, 30, 37, 31, 35, 36, 35, 31, 41, 34, 37, 36, 39, 35, 43, 38, 44, 41, 42, 38, 49, 40, 43

Offset

1,3

Links

Table of n, a(n) for n=1..63.

Formula

G.f.: x+(Sum_{b>=2} (Sum_{k>=0} x^(b^k)/(Sum_{0<=i<b} x^(i*b^k)))/(1-x) - x). If the initial term was 0, the initial "x+" would not be needed. This value is rather arbitrary; changing the "n+1" in the definition to "n" would make it 0. - Franklin T. Adams-Watters, Nov 03 2005

Mathematica

f[n_] := Count[Flatten@ Table[ IntegerDigits[n, b], {b, 2, n + 1}], 1]; Array[f, 63] (* Robert G. Wilson v, Nov 14 2012 *)

Crossrefs

Cf. A053735, A053737, A062756, A077267.

Cf. A033093, A033096, A033097, A033099, A033101, A033103, A033105, A033107, A033109, A033111.

Sequence in context: A274529 A284061 A162625 * A158907 A338281 A338723

Adjacent sequences: A033092 A033093 A033094 * A033096 A033097 A033098

Keyword

nonn,base

Author

Clark Kimberling

Status

approved