A160385 Number of nonzero digits in base-4 representation of n.

0, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 2, 3, 3, 3, 3, 4, 4, 4, 3

Offset

0,6

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) = a(m), a(4m+1) = a(4m+2) = a(4m+3) = 1+a(m).

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

Morphism: 0, j -> j,j+1,j+1,j+1; e.g., 0 -> 0111 -> 0111122212221222 -> ...

Prog

(Haskell)
import Data.List (unfoldr)
a160385 = sum . map (signum . (`mod` 4)) .
unfoldr (\x -> if x == 0 then Nothing else Just (x, x `div` 4))
-- Reinhard Zumkeller, Apr 22 2011

Crossrefs

Sequence in context: A294647 A077099 A276337 * A076881 A355813 A136754

Adjacent sequences: A160382 A160383 A160384 * A160386 A160387 A160388

Keyword

nonn,base,easy

Author

Frank Ruskey, Jun 05 2009

Status

approved