A160383 Number of 3's in base-4 representation of n.

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

Offset

0,16

Links

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

F. T. Adams-Watters and 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+3) = 1+a(m), a(4m) = a(4m+1) = a(4m+2) = a(m).

G.f.: (1/(1-z))*Sum_{m>=0} (z^(3*4^m)*(1 - z^(4^m))/(1 - z^(4^(m+1)))).

Morphism: 0, j -> j,j,j,j+1; e.g., 0 -> 0001 -> 0001000100011112 -> ...

Prog

(PARI) a(n) = #select(x->(x==3), digits(n, 4)); \\ Michel Marcus, Mar 24 2020

Crossrefs

Cf. A007090 (base 4), A160380 (0's), A160381 (1's), A160382 (2's).

Cf. A283316 (mod 2).

Sequence in context: A358345 A258059 A093956 * A330023 A392880 A328891

Adjacent sequences: A160380 A160381 A160382 * A160384 A160385 A160386

Keyword

nonn,base,easy

Author

Frank Ruskey, Jun 05 2009

Status

approved