A236677 a(0)=1; for n>0, a(n) = (1-a(floor(log_2(n)))) * a(n-msb(n)); characteristic function of A079599.

1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1

Offset

0

Comments

This is NOT the leftmost column of A125999, as here a(2^64) = 0, while X_A126002(2^64) = 1.

Links

Antti Karttunen, Table of n, a(n) for n = 0..8192

Formula

a(0) = 1 and for n > 0, a(n) = (1-a(A000523(n))) * a(A053645(n)) [where A000523 gives the bit-index of the most significant bit of n (msb), and A053645 gives n without its msb].

For all n, a(n) * A034798(n) = 0 (as ones in this sequence occur at the positions where zeros are in A034798).

Prog

(Scheme, with Antti Karttunen's IntSeq-library for memoizing definec-macro, two alternative implementations)
(definec (A236677 n) (if (zero? n) 1 (* (- 1 (A236677 (A000523 n))) (A236677 (A053645 n)))))
(definec (A236677 n) (let loop ((n n) (i 0)) (cond ((zero? n) 1) ((odd? n) (if (= 1 (A236677 i)) 0 (loop (/ (- n 1) 2) (+ i 1)))) (else (loop (/ n 2) (+ i 1))))))

Crossrefs

A236678 gives the partial sums. Differs from the characteristic function of A047467 for the first at n=256, as here a(256)=0, while X_A047467(256)=1 because 256 = 0 modulo 8.

Cf. A079599, A034798.

Sequence in context: A154271 A225569 A087032 * A190236 A190224 A352678

Adjacent sequences: A236674 A236675 A236676 * A236678 A236679 A236680

Keyword

nonn

Author

Antti Karttunen, Jan 29 2014

Extensions

Incorrect formula removed by Georg Fischer, Dec 02 2022

Status

approved