A292943 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.

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

Offset: 1

Author

Antti Karttunen, Sep 28 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2048
• Index entries for sequences related to binary expansion of n

Crossrefs

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

Cf. also A292253, A292255, A292383.

Programs

Scheme

(define (A292943 n) (A292944 (A243071 n)))
(define (A292943 n) (if (<= n 1) 0 (+ (if (= 3 (modulo n 6)) 1 0) (* 2 (A292943 (A252463 n))))))

Formula

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

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.

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

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