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A160384
Number of nonzero digits in the base-3 representation of n.
9
0, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 3, 3, 2, 3, 3, 1, 2, 2, 2, 3, 3, 2, 3, 3, 1, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 3, 4, 4, 3, 4, 4, 2, 3, 3, 3, 4, 4, 3, 4, 4, 1, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 3, 4, 4, 3, 4, 4, 2, 3, 3, 3, 4, 4, 3, 4, 4, 1, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 3, 4, 4, 3, 4, 4, 2, 3, 3, 3, 4, 4
OFFSET
0,5
FORMULA
Recurrence relation: a(0) = 0, a(3m) = a(m), a(3m+1) = a(3m+2) = 1+a(m).
G.f.: (1/(1-z))*Sum_{m>=1} (z^(3^(m-1)) - z^(3^m))/(1 - z^(3^m)).
Morphism: 0, j -> j,j+1,j+1; e.g., 0 -> 011 -> 011122122 -> ...
MATHEMATICA
Join[{0}, Table[IntegerLength[n, 3]-DigitCount[n, 3, 0], {n, 110}]] (* Harvey P. Dale, Jun 21 2015 *)
PROG
(PARI) a(n)=my(d=digits(n, 3)); sum(i=1, #d, !!d[i]) \\ Charles R Greathouse IV, Jan 13 2014
CROSSREFS
Sequence in context: A024693 A025126 A129706 * A178305 A338621 A024327
KEYWORD
nonn,base,easy
AUTHOR
Frank Ruskey, Jun 05 2009
STATUS
approved