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%I #11 Jan 15 2015 11:40:11
%S 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,
%T 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,
%U 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
%N 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.
%C 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.
%H Antti Karttunen, <a href="/A253555/b253555.txt">Table of n, a(n) for n = 1..8192</a>
%F a(1) = 0; for n > 1: a(n) = 1 + a(A253554(n)).
%F a(n) = A029837(1+A252754(n)) = A029837(1+A252756(n)).
%F a(n) = A253556(n) + A253557(n).
%F Other identities.
%F For all n >= 1:
%F a(A000079(n)) = n. [I.e., a(2^n) = n.]
%F a(A000040(n)) = n.
%F a(A001248(n)) = n+1.
%F For n >= 2, a(n) = A253558(n) + A253559(n).
%o (Scheme, three versions, first one using memoization macro definec)
%o (definec (A253555 n) (if (<= n 1) 0 (+ 1 (A253555 (A253554 n)))))
%o (define (A253555 n) (A029837 (+ 1 (A252754 n))))
%o (define (A253555 n) (A029837 (+ 1 (A252756 n))))
%Y Cf. A000040, A000079, A001248, A253554.
%Y Cf. also A252753, A252754, A252755, A252756, A253557, A253558, A253559.
%Y Differs from A252464 for the first time at n=21, where a(21) = 4, while A252463(21) = 5.
%K nonn
%O 1,3
%A _Antti Karttunen_, Jan 12 2015
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