|
%I #23 Dec 12 2016 09:11:28
%S 0,1,2,3,2,3,4,3,4,4,5,3,4,5,4,5,4,5,6,5,5,4,5,6,6,5,4,5,6,5,6,5,6,6,
%T 7,5,6,6,6,7,5,6,6,6,5,7,7,6,6,5,7,7,6,7,6,6,7,5,6,7,6,7,6,7,6,7,8,7,
%U 7,6,7,8,7,7,6,7,7,8,6,7,7,7,8,6,7,6,7,8,8,7,7,6,8,7,7,8,6,8,7,7,8,7,6,8,7,8,8,7,7,8,8,6,7,7,7,8,7,8,8,7,6,7,8,7,8,7,8,7
%N a(1) = 0; for n > 1, a(n) = 1 + a(A256992(n)).
%C Number of iterations of A256992 needed to reach one when starting from n.
%H Antti Karttunen, <a href="/A256993/b256993.txt">Table of n, a(n) for n = 1..8192</a>
%F a(1) = 0; for n > 1, a(n) = 1 + a(A256992(n)).
%F Other observations. For all n >= 1 it holds that:
%F a(n) >= A254110(n).
%F a(n) >= A256989(n).
%F a(n) >= A255559(n)-1.
%F Also it seems that a(n) - A070939(n) = -1, 0 or +1 for all n >= 1. [Compare A256991 and A256992 to see the connection.]
%F It is also very likely that a(n) <= A071542(n) for all n.
%F From _Antti Karttunen_, Dec 10 2016: (Start)
%F For all n >= 2, a(n) = A070939(A279341(n)) = A070939(A279343(n)).
%F For all n >= 2, a(n) = A279345(n) + A279346(n) - 1.
%F (End)
%o (Scheme, with memoization macro definec)
%o (definec (A256993 n) (if (= 1 n) 0 (+ 1 (A256993 (A256992 n)))))
%Y Cf. A070939, A071542, A254110, A255559, A256991, A256992, A257264, A257265, A279341, A279343, A279345, A279346.
%K nonn
%O 1,3
%A _Antti Karttunen_, Apr 15 2015
|
