A253559 a(1) = 0; for n>1: a(n) = A253557(n) - 1.

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

Author

Antti Karttunen, Jan 12 2015

Keywords

• nonn

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

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

Crossrefs

Essentially, one less than A253557.

A008578 gives the positions of zeros.

Cf. A000120, A080791, A252753, A252754, A252755, A252756, A253554, A253555, A253556, A253558.

Differs from A252736 for the first time at n=21, where a(21) = 2, while A252736(21) = 1.

Programs

Scheme

(define (A253559 n) (if (= 1 n) 0 (+ -1 (A253557 n))))

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).