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

Author

Frank Ruskey, Jun 05 2009

Keywords

• nonn
• base
• easy

Links

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

Programs

Mathematica

Join[{0},Table[IntegerLength[n,3]-DigitCount[n,3,0],{n,110}]] (* Harvey P. Dale, Jun 21 2015 *)

PARI

a(n)=my(d=digits(n,3)); sum(i=1,#d,!!d[i]) \\ Charles R Greathouse IV, Jan 13 2014

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 -> ...