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A087069 a(n) = Sum_{k >= 0} floor(n/(4^k)). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
Essentially partial sums of A115362.
Sequence in context: A242491 A038129 A062071 * A023737 A037459 A020654
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 07 2003
STATUS
approved

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Last modified April 14 20:39 EDT 2024. Contains 371667 sequences. (Running on oeis4.)