A087069 a(n) = Sum_{k >= 0} floor(n/(4^k)).

0, 1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 42, 43, 44, 45, 47, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 65, 66, 68, 69, 70, 71, 73, 74, 75, 76, 78, 79, 80, 81, 85, 86, 87, 88, 90, 91, 92, 93

Offset

0,3

Links

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

Formula

a(n) = Sum_{k>=0} A030308(n,k)*A000975(k+1). - Philippe Deléham, Oct 16 2011

a(n) = A054893(4*n). - Vaclav Kotesovec, May 28 2014

G.f.: (1/(1 - x))*Sum_{k>=0} x^(4^k)/(1 - x^(4^k)). - Ilya Gutkovskiy, Mar 15 2018

Example

a(4) = 4 + floor(4/4) + floor(4/16) + floor(4/64) + ... = 5.

Mathematica

Table[Sum[Floor[n/4^k], {k, 0, 1000}], {n, 0, 50}] (* G. C. Greubel, Oct 11 2017 *)

Prog

(Haskell)
import Data.List (unfoldr)
a087069 =
   sum . unfoldr (\x -> if x == 0 then Nothing else Just (x, x `div` 4))
-- Reinhard Zumkeller, Apr 22 2011
(PARI) for(n=0, 50, print1(sum(k=0, 1000, floor(n/4^k)), ", ")) \\ G. C. Greubel, Oct 11 2017

Crossrefs

Cf. A005187, A054893, A242954.

Essentially partial sums of A115362.

Sequence in context: A242491 A038129 A062071 * A023737 A037459 A020654

Adjacent sequences: A087066 A087067 A087068 * A087070 A087071 A087072

Keyword

nonn

Author

Clark Kimberling, Aug 07 2003

Status

approved