A160384 Number of nonzero digits in the base-3 representation of n.

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

Links

Table of n, a(n) for n=0..104.

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(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

Adjacent sequences: A160381 A160382 A160383 * A160385 A160386 A160387

Keyword

nonn,base,easy

Author

Frank Ruskey, Jun 05 2009

Status

approved