A160380 a(0) = 0; for n >= 1, a(n) = number of 0's in base-4 representation of n.

0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 1, 1, 1, 0, 0, 0, 1

Offset

0,17

Comments

The base-4 representation of 0 is 0, and contains a single zero. - N. J. A. Sloane, Apr 26 2021

Links

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

F. T. Adams-Watters, F. Ruskey, Generating Functions for the Digital Sum and Other Digit Counting Sequences, JIS 12 (2009) 09.5.6

Formula

Recurrence relation: a(0) = 0, a(4m) = 1+a(m), a(4m+1) = a(4m+2) = a(4m+3) = a(m).

Generating function: (1/(1-z))*Sum_{m>=0} (z^(4^(m+1))*(1 - z^(4^m))/(1 - z^(4^(m+1)))).

Mathematica

Join[{0}, Table[DigitCount[n, 4, 0], {n, 110}]] (* Harvey P. Dale, Oct 18 2015 *)

Prog

(Haskell)
import Data.List (unfoldr)
a160380 = sum . map ((0 ^ ) . (`mod` 4)) .
   unfoldr (\x -> if x == 0 then Nothing else Just (x, x `div` 4))
-- Reinhard Zumkeller, Apr 22 2011
(PARI) a(n) = #select(x->(x==0), digits(n, 4)); \\ Michel Marcus, Apr 26 2021

Crossrefs

Cf. A007090, A023416, A077267.

Sequence in context: A345008 A316866 A277007 * A122433 A056977 A309144

Adjacent sequences: A160377 A160378 A160379 * A160381 A160382 A160383

Keyword

nonn,base,easy

Author

Frank Ruskey, Jun 05 2009

Extensions

Definition clarified by Georg Fischer, Apr 26 2021

Status

approved