A275727 a(0) = 0, for n >= 1, a(n) = A275736(n) + 2*a(A257684(n)).

0, 1, 2, 3, 2, 3, 4, 5, 6, 7, 6, 7, 4, 5, 6, 7, 6, 7, 4, 5, 6, 7, 6, 7, 8, 9, 10, 11, 10, 11, 12, 13, 14, 15, 14, 15, 12, 13, 14, 15, 14, 15, 12, 13, 14, 15, 14, 15, 8, 9, 10, 11, 10, 11, 12, 13, 14, 15, 14, 15, 12, 13, 14, 15, 14, 15, 12, 13, 14, 15, 14, 15, 8, 9, 10, 11, 10, 11, 12, 13, 14, 15, 14, 15, 12, 13, 14, 15

Offset

0,3

Comments

a(n) has ones in those positions of its base-2 representation where n has nonzero digits in its factorial base representation.

Links

Antti Karttunen, Table of n, a(n) for n = 0..40320

Index entries for sequences related to binary expansion of n

Index entries for sequences related to factorial base representation

Formula

a(0) = 0, for n >= 1, a(n) = A275736(n) + 2*a(A257684(n)).

a(n) = A048675(A275733(n)).

Other identities and observations. For all n >= 0:

A000120(a(n)) = A060130(n).

Example

For n=19, A007236(19) = 301, thus a(19) = 5 because A007088(5) = 101.

Prog

(Scheme, with memoization-macro definec)
(definec (A275727 n) (if (zero? n) n (+ (A275736 n) (* 2 (A275727 (A257684 n))))))
(define (A275727 n) (A048675 (A275733 n)))

Crossrefs

Cf. A000120, A007088, A007623, A048675, A060130, A257684, A275733, A275736.

Cf. also A275728.

Sequence in context: A286717 A162751 A026342 * A255395 A175266 A320053

Adjacent sequences: A275724 A275725 A275726 * A275728 A275729 A275730

Keyword

nonn,base,look

Author

Antti Karttunen, Aug 09 2016

Status

approved