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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).
6
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
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.
Sequence in context: A364197 A097291 A269501 * A274515 A362500 A291564
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 23 2015
STATUS
approved