A292946 a(n) = A292945(A163511(n)).

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, 4, 5, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 8, 8, 8, 8, 8, 8, 10, 10, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, 4, 5, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0

Offset

0,15

Comments

Because A292945(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+5 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 formulas just restate 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) = A292945(A163511(n)).

a(n) = A292264(n) AND (A292256(n) XOR A292274(n)), where AND is bitwise-and (A004198) and XOR is bitwise-XOR (A003987).

a(n) = A292264(n) AND (A292254(n) XOR A292271(n)). [See comments.]

For all n >= 0, A292942(n) + A292944(n) + a(n) = n.

Prog

(Scheme) (define (A292946 n) (A292945 (A163511 n)))

Crossrefs

Cf. A005940, A163511, A292945.

Cf. also A292247, A292248, A292254, A292256, A292264, A292271, A292274, A292592, A292593, A292942, A292944 (for similarly constructed sequences).

Sequence in context: A276009 A328842 A113302 * A196078 A287086 A180823

Adjacent sequences: A292943 A292944 A292945 * A292947 A292948 A292949

Keyword

nonn

Author

Antti Karttunen, Sep 28 2017

Status

approved