A332899 a(1) = 0, and for n > 2, a(n) = a(A332893(n)) + A000035(n).

0, 1, 2, 1, 3, 2, 4, 1, 2, 3, 6, 2, 5, 4, 3, 1, 7, 2, 8, 3, 4, 6, 10, 2, 3, 5, 2, 4, 9, 3, 12, 1, 6, 7, 4, 2, 11, 8, 5, 3, 13, 4, 14, 6, 3, 10, 16, 2, 4, 3, 7, 5, 15, 2, 6, 4, 8, 9, 18, 3, 17, 12, 4, 1, 5, 6, 20, 7, 10, 4, 22, 2, 19, 11, 3, 8, 6, 5, 24, 3, 2, 13, 26, 4, 7, 14, 9, 6, 21, 3, 5, 10, 12, 16, 8, 2, 23, 4, 6, 3, 25, 7, 28, 5, 4

Offset: 1

Author

Antti Karttunen, Mar 04 2020

Keywords

• nonn

Comments

a(n) tells how many odd numbers are encountered when map x -> A332893(x) is used to traverse from n to 1, the root of the binary tree A332815. This count includes both the starting n itself if it is odd, but excludes 1 where the iteration ends.

a(n) also gives the index of the largest prime factor (A061395) in A332808(n), which is the inverse permutation of A108548 (see also A108546).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A000035, A061395, A080791, A332808, A332811, A332815, A332816, A332893, A332894, A332897, A332898.

Cf. A000079 (after its initial term, gives the positions of 1's).

Programs

PARI

A332899(n) = if(1==n,0,A332899(A332893(n)) + (n%2));

Formula

a(1) = 0, and for n > 1, a(n) = a(A332893(n)) + A000035(n).

a(n) = A000120(A332811(n)).

a(n) = A061395(A332808(n)).

a(n) = A332897(n) + A332898(n).

a(n) <= A332894(n).

For all n > 1, a(n) = 1 + A080791(A332816(n)).