cp's OEIS Frontend

A253558 a(n) = A253556(n) + 1.

%I A253558 #10 Jan 15 2015 11:40:39
%S A253558 1,1,2,1,3,2,4,1,2,3,5,2,6,4,3,1,7,2,8,3,2,5,9,2,3,6,4,4,10,3,11,1,3,
%T A253558 7,4,2,12,8,5,3,13,2,14,5,2,9,15,2,4,3,3,6,16,4,3,4,4,10,17,3,18,11,6,
%U A253558 1,5,3,19,7,3,4,20,2,21,12,7,8,5,5,22,3,5,13,23,2,4,14,4,5,24,2,4,9,2,15,6,2,25,4,8,3,26,3
%N A253558 a(n) = A253556(n) + 1.
%C A253558 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 at), a(n) gives the number of odd numbers encountered on the path (i.e., including both the final 1 and the starting n if it was odd).
%H A253558 Antti Karttunen, <a href="/A253558/b253558.txt">Table of n, a(n) for n = 1..8192</a>
%F A253558 a(n) = A253556(n) + 1.
%F A253558 a(n) = A080791(A252754(n)) + 1. [One more than the number of nonleading 0-bits in A252754(n).]
%F A253558 Other identities.
%F A253558 For all n >= 1:
%F A253558 a(A000040(n)) = n.
%F A253558 For all n >= 2:
%F A253558 a(n) = A000120(A252756(n)). [Binary weight of A252756(n).]
%F A253558 a(n) = A253555(n) - A253559(n).
%o A253558 (Scheme) (define (A253558 n) (+ 1 (A253556 n)))
%Y A253558 One more than A253556.
%Y A253558 Powers of two, A000079, gives the positions of ones.
%Y A253558 Cf. A000040, A253555, A253557, A253559.
%Y A253558 After n=1, differs from A061395 for the first time at n=21, where a(21) = 2, while A061395(21) = 4.
%K A253558 nonn
%O A253558 1,3
%A A253558 _Antti Karttunen_, Jan 12 2015