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A253559
a(1) = 0; for n>1: a(n) = A253557(n) - 1.
7
0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 2, 0, 1, 1, 3, 0, 2, 0, 2, 2, 1, 0, 3, 1, 1, 1, 2, 0, 2, 0, 4, 2, 1, 1, 3, 0, 1, 1, 3, 0, 3, 0, 2, 3, 1, 0, 4, 1, 2, 2, 2, 0, 2, 2, 3, 2, 1, 0, 3, 0, 1, 1, 5, 1, 3, 0, 2, 3, 2, 0, 4, 0, 1, 1, 2, 1, 2, 0, 4, 2, 1, 0, 4, 2, 1, 2, 3, 0, 4, 2, 2, 4, 1, 1, 5, 0, 2, 1, 3, 0, 3, 0, 3, 3, 1, 0, 3, 0, 3, 1, 4, 0, 3, 3, 2, 3, 1, 1, 4, 1, 1, 3, 2, 2, 2, 0, 6
OFFSET
1,8
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 > 2 encountered on the path (i.e., excluding the 2 from the count but including the starting n if it was even).
LINKS
FORMULA
a(n) = A080791(A252756(n)). [Number of nonleading 0-bits in A252756(n).]
a(1) = 0; for n>1: a(n) = A253557(n) - 1.
Other identities. For all n >= 2:
a(n) = A000120(A252754(n)) - 1. [One less than the binary weight of A252754(n).]
a(n) = A253555(n) - A253558(n).
PROG
(Scheme) (define (A253559 n) (if (= 1 n) 0 (+ -1 (A253557 n))))
CROSSREFS
Essentially, one less than A253557.
A008578 gives the positions of zeros.
Differs from A252736 for the first time at n=21, where a(21) = 2, while A252736(21) = 1.
Sequence in context: A308427 A252736 A351416 * A136167 A140748 A185305
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 12 2015
STATUS
approved