%I #19 Oct 13 2017 05:55:16

%S 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,

%T 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,

%U 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

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

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

%C For n >= 1, a(n) is the length of binary representation of n reduced modulo 3. - _Antti Karttunen_, Oct 10 2017

%H Antti Karttunen, <a href="/A230629/b230629.txt">Table of n, a(n) for n = 0..32768</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F 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

%p 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)];

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

%o (Scheme, with memoization-macro definec)

%o (definec (A230629 n) (if (zero? n) n (modulo (+ 1 (A230629 (/ (- n (if (even? n) 0 1)) 2))) 3))) ;; _Antti Karttunen_, Oct 10 2017

%Y See A230630 for another version.

%Y Cf. A000523.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Oct 30 2013