A292943 - OEIS

%I #9 Sep 30 2017 16:07:22

%S 0,0,1,0,2,2,4,0,1,4,8,4,16,8,5,0,32,2,64,8,9,16,128,8,2,32,1,16,256,

%T 10,512,0,17,64,10,4,1024,128,33,16,2048,18,4096,32,9,256,8192,16,4,4,

%U 65,64,16384,2,18,32,129,512,32768,20,65536,1024,17,0,34,34,131072,128,257,20,262144,8,524288,2048,5,256,20,66,1048576,32,1,4096

%N a(n) = A292944(A243071(n)); Base-2 expansion of a(n) encodes the steps where numbers of the form 6k+3 are encountered when map x -> A252463(x) is iterated down to 1, starting from x=n.

%H Antti Karttunen, <a href="/A292943/b292943.txt">Table of n, a(n) for n = 1..2048</a>

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

%F a(n) = A292944(A243071(n)).

%F a(1) = 0, and for n > 1, a(n) = 2*a(A252463(n)) + [n == 3 (mod 6)], where the last part of the formula is Iverson bracket, giving 1 only if n is of the form 6k+3, and 0 otherwise.

%F For n >= 0, a(A163511(n)) = A292944(n).

%F For n >= 1, A292941(n) + a(n) + A292945(n) = a(n) + A292253(n) + A292255(n) = A243071(n).

%o (Scheme)

%o (define (A292943 n) (A292944 (A243071 n)))

%o (define (A292943 n) (if (<= n 1) 0 (+ (if (= 3 (modulo n 6)) 1 0) (* 2 (A292943 (A252463 n))))))

%Y Cf. A005940, A163511, A243071, A292941, A292944, A292945.

%Y Cf. also A292253, A292255, A292383.

%K nonn

%O 1,5

%A _Antti Karttunen_, Sep 28 2017