

A253557


a(1) = 0; after which, a(2n) = 1 + a(n), a(2n+1) = a(A250470(n)).


5



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

1,4


COMMENTS

Consider the binary trees illustrated in A252753 and A252755: If we start from any n, computing successive iterations of A253554 until 1 is reached (i.e., we are traversing level by level towards the root of the tree, starting from that vertex of the tree where n is located), a(n) gives the number of even numbers encountered on the path (i.e., including both 2 and the starting n if it was even).


LINKS

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


FORMULA

a(1) = 0; after which, a(2n) = 1 + a(n), a(2n+1) = a(A250470(n)).
a(n) = A253555(n)  A253556(n).
a(n) = A000120(A252754(n)). [Binary weight of A252754(n).]
Other identities.
For all n >= 0:
a(2^n) = n.
For all n >= 2:
a(n) = A080791(A252756(n)) + 1. [One more than the number of nonleading 0bits in A252756(n).]


PROG

(Scheme)
(definec (A253557 n) (cond ((= 1 n) 0) ((odd? n) (A253557 (A250470 n))) (else (+ 1 (A253557 (/ n 2))))))


CROSSREFS

Essentially, one more than A253559.
Primes, A000040, gives the positions of ones.
Cf. A000079, A000120, A080791, A252753, A252754, A252755, A252756, A253554, A253555, A253556, A253558.
Differs from A001222 for the first time at n=21, where a(21) = 3, while A001222(21) = 2.
Sequence in context: A086436 A001222 A257091 * A098893 A069248 A008481
Adjacent sequences: A253554 A253555 A253556 * A253558 A253559 A253560


KEYWORD

nonn


AUTHOR

Antti Karttunen, Jan 12 2015


STATUS

approved



