A257248 a(1) = 0; and for n > 1, if A079559(n) = 1, then a(n) = 1 + a(A213714(n)-1), otherwise a(n) = a(A234017(n)).

0, 0, 1, 1, 0, 1, 2, 2, 1, 1, 2, 0, 1, 2, 3, 3, 2, 2, 2, 1, 1, 3, 1, 2, 2, 3, 0, 1, 2, 3, 4, 4, 3, 3, 3, 2, 2, 3, 2, 2, 2, 4, 1, 1, 3, 2, 3, 1, 3, 4, 2, 2, 1, 2, 3, 3, 4, 0, 1, 2, 3, 4, 5, 5, 4, 4, 4, 3, 3, 4, 3, 3, 3, 4, 2, 2, 3, 3, 3, 2, 3, 5, 2, 2, 2, 2, 4, 4, 3, 1, 1, 3, 2, 4, 2, 3, 4, 5, 1, 3, 3, 3, 4, 2, 3, 2, 2, 1, 4, 4, 2, 5, 1, 3, 3, 2, 3, 4, 4, 5, 0, 1, 2, 3, 4, 5, 6, 6

Offset

1,7

Comments

a(n) tells how many nonzero terms of A005187 are encountered when traversing toward the root of binary tree A233276, starting from the node containing n and before 1 is reached. This count includes both n (in case it is a term of A005187) but excludes the 1 and 0 at the root. See also comments in A257249, A256478 and A256991.

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

Formula

a(1) = 0; and for n > 1, if A079559(n) = 1, then a(n) = 1 + a(A213714(n)-1), otherwise a(n) = a(A234017(n)).

a(n) = A080791(A233275(n)). [Number of nonleading zeros in the binary representation of A233275(n).]

Other identities. For all n >= 1:

a(n) = A256478(n)-1 = A000120(A233277(n))-1.

a(n) = A070939(n) - A257249(n).

Prog

(Scheme, alternative definitions, the first one utilizing memoizing definec-macro)
(definec (A257248 n) (if (= 1 n) 0 (+ (A079559 n) (A257248 (if (zero? (A079559 n)) (A234017 n) (+ -1 (A213714 n)))))))
(define (A257248 n) (- (A256478 n) 1))

Crossrefs

One less than A256478.

Cf. A000120, A000325, A005187, A070939, A079559, A080791, A213714, A234017, A233275, A233276, A233277, A255559, A257249, A256991.

Sequence in context: A318191 A208183 A214810 * A090737 A204016 A343334

Adjacent sequences: A257245 A257246 A257247 * A257249 A257250 A257251

Keyword

nonn

Author

Antti Karttunen, Apr 19 2015

Status

approved