A160382 Number of 2's in base-4 representation of n.

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

Offset

0,11

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

Generating function: (1/(1-z))*Sum_{m>=0} (z^(2*4^m)*(1 - z^(4^m))/(1 - z^(4^(m+1)))).

Morphism: 0, j -> j,j,j+1,j; e.g., 0 -> 0010 -> 0010110111210010 -> ...

Prog

(PARI) a(n) = #select(x->(x==2), digits(n, 4)); \\ Michel Marcus, Mar 24 2020

Crossrefs

Cf. A007090.

Sequence in context: A025435 A304685 A186714 * A336352 A081221 A366988

Adjacent sequences: A160379 A160380 A160381 * A160383 A160384 A160385

Keyword

nonn,base,easy

Author

Frank Ruskey, Jun 05 2009

Status

approved