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

1,3

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

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)).

Prog

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

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).

Sequence in context: A295877 A336395 A336393 * A331521 A244967 A124172

Adjacent sequences: A332896 A332897 A332898 * A332900 A332901 A332902

Keyword

nonn

Author

Antti Karttunen, Mar 04 2020

Status

approved