A254044 a(1) = 1, for n>1: a(n) = a(A253889(n)) + (1 if n is of the form 3n or 3n+1, otherwise 0).

1, 1, 2, 2, 1, 3, 3, 2, 3, 2, 2, 3, 2, 1, 4, 4, 3, 4, 5, 3, 3, 3, 2, 4, 3, 3, 5, 3, 2, 4, 5, 2, 2, 5, 3, 3, 4, 2, 3, 3, 1, 5, 4, 4, 4, 5, 4, 4, 4, 3, 3, 4, 4, 5, 5, 5, 5, 4, 3, 2, 3, 3, 4, 4, 3, 7, 4, 2, 3, 3, 4, 4, 3, 3, 4, 4, 3, 5, 5, 5, 6, 5, 3, 4, 5, 2, 5, 4, 4, 5, 5, 5, 5, 5, 2, 5, 7, 2, 3, 4, 5, 5, 6, 3, 6, 5, 3, 6, 3, 4, 5, 5, 2, 7, 5, 3, 5, 2, 3, 5, 7, 1, 4, 6, 5, 5, 3, 4

Offset

1,3

Links

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

Formula

a(1) = 1, for n>1: a(n) = a(A253889(n)) + [n is of the form 3n or 3n+1, i.e., in A032766] (Here [ ] is Iverson bracket).

a(1) = 0, thereafter, if n = 3k+2, then a(n) = a((n+1)/3), otherwise a(n) = 1 + a(A253889(n)).

a(n) = A000120(A064216(n)). [Binary weight of terms of A064216.]

a(n) = A253894(n) - A254045(n).

Other identities:

a(A007051(n)) = 1 for all n >= 0. [And no 1's in any other positions.]

Prog

(Scheme, two versions using memoization-macro definec)
(definec (A254044 n) (if (= 1 n) 1 (+ (A254044 (A253889 n)) (- 1 (floor->exact (/ (modulo n 3) 2))))))
(definec (A254044 n) (cond ((= 1 n) 1) ((= 2 (modulo n 3)) (A254044 (/ (+ 1 n) 3))) (else (+ 1 (A254044 (A253889 n))))))
;; Alternatively:
(define (A254044 n) (A000120 (A064216 n)))

Crossrefs

Positions of ones: A007051.

Cf. A000120, A032766, A064216, A253889, A253894, A254045.

Sequence in context: A364197 A097291 A269501 * A274515 A362500 A291564

Adjacent sequences: A254041 A254042 A254043 * A254045 A254046 A254047

Keyword

nonn

Author

Antti Karttunen, Jan 23 2015

Status

approved