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A160385
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Number of nonzero digits in base-4 representation of n.
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3
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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
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,6
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LINKS
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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
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FORMULA
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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 -> ...
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PROG
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(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
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CROSSREFS
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Sequence in context: A294647 A077099 A276337 * A076881 A136754 A276788
Adjacent sequences: A160382 A160383 A160384 * A160386 A160387 A160388
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KEYWORD
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nonn,base,easy
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AUTHOR
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Frank Ruskey, Jun 05 2009
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STATUS
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approved
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