A277808 a(n) = number of iterations of map k -> A003188(A006068(k)/2) that are required (when starting from k = n) until k is an odious number.

0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 0, 1, 2, 0, 3, 0, 0, 1, 4, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 4, 0, 0, 1, 0, 1, 2, 0, 5, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 0, 1, 2, 0, 3, 0, 0, 1, 4, 0, 0, 1, 0, 1, 2, 0, 5, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 6, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 0, 1, 2, 0, 3, 0, 0, 1, 4

Offset: 1

Author

Antti Karttunen, Nov 03 2016

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to binary expansion of n

Crossrefs

One less than A277822.

A left inverse of A003945.

Cf. A277812 (gives the odious number where such an iteration is finished at when starting from k=n).

Cf. A000069, A001969, A001511, A003188, A006068, A010059, A010060, A245710, A268389.

Formula

a(n) = A010059(n) * A001511(n).

If A010060(n) = 1 [when n is one of the odious numbers, A000069], then a(n) = 0, otherwise a(n) = 1 + a(A003188(A006068(n)/2)).

Other identities:

For all n >= 0, a(A003945(n)) = n.