A253555 a(1) = 0, a(2n) = 1 + a(n), a(2n+1) = 1 + a(A250470(2n+1)); also binary width of terms of A252754 and A252756.

0, 1, 2, 2, 3, 3, 4, 3, 3, 4, 5, 4, 6, 5, 4, 4, 7, 4, 8, 5, 4, 6, 9, 5, 4, 7, 5, 6, 10, 5, 11, 5, 5, 8, 5, 5, 12, 9, 6, 6, 13, 5, 14, 7, 5, 10, 15, 6, 5, 5, 5, 8, 16, 6, 5, 7, 6, 11, 17, 6, 18, 12, 7, 6, 6, 6, 19, 9, 6, 6, 20, 6, 21, 13, 8, 10, 6, 7, 22, 7, 7, 14, 23, 6, 6, 15, 6, 8, 24, 6, 6, 11, 6, 16, 7, 7, 25, 6, 9, 6

Offset: 1

Author

Antti Karttunen, Jan 12 2015

Keywords

• nonn

Comments

a(n) tells how many iterations of A253554 are needed before 1 is reached, i.e., the distance of n from 1 in binary trees like A252753 and A252755.

Links

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

Crossrefs

Cf. A000040, A000079, A001248, A253554.

Cf. also A252753, A252754, A252755, A252756, A253557, A253558, A253559.

Differs from A252464 for the first time at n=21, where a(21) = 4, while A252463(21) = 5.

Formula

a(1) = 0; for n > 1: a(n) = 1 + a(A253554(n)).

a(n) = A029837(1+A252754(n)) = A029837(1+A252756(n)).

a(n) = A253556(n) + A253557(n).

Other identities.

For all n >= 1:

a(A000079(n)) = n. [I.e., a(2^n) = n.]

a(A000040(n)) = n.

a(A001248(n)) = n+1.

For n >= 2, a(n) = A253558(n) + A253559(n).