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A332894 a(1) = 0, a(2n) = 1 + a(n), a(2n+1) = 1 + a(A332819(2n+1)); also binary width of terms of A332816.

%I A332894 #14 Mar 04 2020 18:08:46
%S A332894 0,1,2,2,3,3,4,3,3,4,6,4,5,5,4,4,7,4,8,5,5,7,10,5,4,6,4,6,9,5,12,5,7,
%T A332894 8,5,5,11,9,6,6,13,6,14,8,5,11,16,6,5,5,8,7,15,5,7,7,9,10,18,6,17,13,
%U A332894 6,6,6,8,20,9,11,6,22,6,19,12,5,10,7,7,24,7,5,14,26,7,8,15,10,9,21,6,6,12,13,17,9,7,23,6,8,6,25,9,28,8,6
%N A332894 a(1) = 0, a(2n) = 1 + a(n), a(2n+1) = 1 + a(A332819(2n+1)); also binary width of terms of A332816.
%C A332894 a(n) tells how many iterations of A332893 are needed before 1 is reached, i.e., the distance of n from 1 in binary trees like A332815.
%C A332894 Each n > 0 occurs 2^(n-1) times in total.
%H A332894 Antti Karttunen, <a href="/A332894/b332894.txt">Table of n, a(n) for n = 1..65537</a>
%F A332894 a(n) = A252464(A332808(n)).
%F A332894 a(1) = 0, and for n > 1, a(n) = 1 + a(A332893(n)).
%F A332894 For n >= 1, a(A108546(n)) = n; for all n >= 0, a(2^n) = n.
%F A332894 For n > 1: (Start)
%F A332894 a(n) = 1 + a(n/2) if n is even, and a(n) = 1 + a(A332819(n)), if n is odd.
%F A332894 a(n) = A070939(A332816(n)).
%F A332894 a(n) >= A332899(n).
%F A332894 (End)
%o A332894 (PARI) A332894(n) = if(1==n,0,if(!(n%2),1+A332894(n/2),1+A332894(A332819(n))));
%o A332894 (PARI) A332894(n) = if(1==n,0,1+A332894(A332893(n)));
%Y A332894 A left inverse of A000079 and A108546.
%Y A332894 Cf. A070939, A252464, A332808, A332815, A332816, A332819, A332893, A332897, A332898, A332899.
%K A332894 nonn
%O A332894 1,3
%A A332894 _Antti Karttunen_, Mar 04 2020