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
Keywords
Examples
a(4) = 4 + floor(4/4) + floor(4/16) + floor(4/64) + ... = 5.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Programs
-
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
-
Mathematica
Table[Sum[Floor[n/4^k], {k, 0, 1000}], {n, 0, 50}] (* G. C. Greubel, Oct 11 2017 *) -
PARI
for(n=0,50, print1(sum(k=0,1000, floor(n/4^k)), ", ")) \\ G. C. Greubel, Oct 11 2017
Formula
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