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

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, 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, 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

Offset

1,3

Comments

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.

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

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

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

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

For n > 1: (Start)

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

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

a(n) >= A332899(n).

(End)

Prog

(PARI) A332894(n) = if(1==n, 0, if(!(n%2), 1+A332894(n/2), 1+A332894(A332819(n))));
(PARI) A332894(n) = if(1==n, 0, 1+A332894(A332893(n)));

Crossrefs

A left inverse of A000079 and A108546.

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

Sequence in context: A252464 A324861 A324863 * A269989 A057935 A292042

Adjacent sequences: A332891 A332892 A332893 * A332895 A332896 A332897

Keyword

nonn

Author

Antti Karttunen, Mar 04 2020

Status

approved