1,3

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.

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

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).

(Scheme, three versions, first one using memoization macro definec)

(definec (A253555 n) (if (<= n 1) 0 (+ 1 (A253555 (A253554 n)))))

(define (A253555 n) (A029837 (+ 1 (A252754 n))))

(define (A253555 n) (A029837 (+ 1 (A252756 n))))

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.

Sequence in context: A230697 A322163 A075167 * A252464 A269989 A057935

Adjacent sequences: A253552 A253553 A253554 * A253556 A253557 A253558

nonn

Antti Karttunen, Jan 12 2015

approved