A332894 - OEIS

%I #14 Mar 04 2020 18:08:46

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

%C 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 Each n > 0 occurs 2^(n-1) times in total.

%H Antti Karttunen, <a href="/A332894/b332894.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = A252464(A332808(n)).

%F a(1) = 0, and for n > 1, a(n) = 1 + a(A332893(n)).

%F For n >= 1, a(A108546(n)) = n; for all n >= 0, a(2^n) = n.

%F For n > 1: (Start)

%F a(n) = 1 + a(n/2) if n is even, and a(n) = 1 + a(A332819(n)), if n is odd.

%F a(n) = A070939(A332816(n)).

%F a(n) >= A332899(n).

%F (End)

%o (PARI) A332894(n) = if(1==n,0,if(!(n%2),1+A332894(n/2),1+A332894(A332819(n))));

%o (PARI) A332894(n) = if(1==n,0,1+A332894(A332893(n)));

%Y A left inverse of A000079 and A108546.

%Y Cf. A070939, A252464, A332808, A332815, A332816, A332819, A332893, A332897, A332898, A332899.

%K nonn

%O 1,3

%A _Antti Karttunen_, Mar 04 2020