A230629 - OEIS

A230629

a(0) = 0; thereafter a(n) = (1 + a(floor(n/2))) mod 3.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

For 0 < 2^i <= n < 2^(i+1), a(n) = ((i+1) mod 3).

For n >= 1, a(n) is the length of binary representation of n reduced modulo 3. - Antti Karttunen, Oct 10 2017

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..32768

Index entries for sequences related to binary expansion of n

FORMULA

G.f. g(z) satisfies: g(z) = z + 2*z^2 + 2*z^3 + (1 + z + ... + z^7)*g(z^8). - Robert Israel, Oct 10 2017

MAPLE

f:=proc(n) option remember; if n=0 then 0 else (1+f(floor(n/2))) mod 3; fi; end; [seq(f(n), n=0..120)];

MATHEMATICA

Join[{0}, Table[Mod[Floor[Log[2, n]] + 1, 3], {n, 80}]] (* Alonso del Arte, Oct 10 2017 *)

PROG

(Scheme, with memoization-macro definec)

(definec (A230629 n) (if (zero? n) n (modulo (+ 1 (A230629 (/ (- n (if (even? n) 0 1)) 2))) 3))) ;; Antti Karttunen, Oct 10 2017

CROSSREFS

See A230630 for another version.

Cf. A000523.

Sequence in context: A248640 A376562 A281083 * A027359 A236109 A279279

Adjacent sequences: A230626 A230627 A230628 * A230630 A230631 A230632

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 30 2013

STATUS

approved