A292942 - OEIS

A292942

a(n) = A292941(A163511(n)).

0, 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 9, 8, 8, 8, 9, 16, 16, 16, 16, 16, 16, 18, 19, 16, 16, 16, 16, 16, 16, 18, 18, 32, 32, 32, 33, 32, 32, 32, 33, 32, 32, 32, 32, 36, 36, 38, 39, 32, 32, 32, 33, 32, 32, 32, 32, 32, 32, 32, 33, 36, 36, 36, 37, 64, 64, 64, 64, 64, 64, 66, 67, 64, 64, 64, 64, 64, 64, 66, 66, 64, 64, 64, 65, 64, 64, 64, 65, 72, 72, 72, 72, 76, 76

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

OFFSET

0,3

COMMENTS

Because A292941(n) = a(A243071(n)), the sequence works as a "masking function" where the 1-bits in a(n) (always a subset of the 1-bits in binary expansion of n) indicate which numbers are of the form 6k+1 in binary tree A163511 (or its mirror image tree A005940) on that trajectory which leads from the root of the tree to the node containing A163511(n).

The AND - XOR formula is just a restatement of the fact that J(-3|n) = J(-1|n)*J(3|n), as the Jacobi-symbol is multiplicative (also) with respect to its upper argument.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8191

Index entries for sequences related to binary expansion of n

Index entries for sequences computed from indices in prime factorization

FORMULA

a(n) = A292941(A163511(n)).

a(n) = A292264(n) AND (A292254(n) XOR A292274(n)), where AND is bitwise-and (A004198) and XOR is bitwise-XOR (A003987). [See comments.]

For all n >= 0, a(n) + A292944(n) + A292946(n) = n.

PROG

(Scheme) (define (A292942 n) (A292941 (A163511 n)))

CROSSREFS

Cf. A005940, A163511, A292941.