A277822 a(n) = index of the column where n is located in array A277880.

0, 1, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 4, 1, 1, 2, 1, 2, 3, 1, 4, 1, 1, 2, 5, 1, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 4, 1, 1, 2, 5, 1, 1, 2, 1, 2, 3, 1, 6, 1, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 4, 1, 1, 2, 1, 2, 3, 1, 4, 1, 1, 2, 5, 1, 1, 2, 1, 2, 3, 1, 6, 1, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 4, 1, 1, 2, 7, 1, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 4, 1, 1, 2, 1, 2, 3, 1, 4, 1, 1, 2, 5

Offset: 0

Author

Antti Karttunen, Nov 03 2016

Keywords

• nonn
• base

Comments

Ordinal transform of A277813.

a(n) = 1 + the number of iterations of map k -> A003188(A006068(k)/2) that are required (when starting from k = n) until k is an odious number.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384
• Index entries for sequences related to binary expansion of n

Crossrefs

One more than A277808.

Cf. A000069, A001969, A001511, A003188, A006068, A010059, A010060, A245710, A277813, A277818, A277880.

Formula

a(0) = 0, for n >= 1, a(n) = 1 + (A010059(n)*A001511(n)).

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

Other identities. For all n >= 1:

a(n) = 1 + a(floor(n/2)) when A010060(n) = 0.

a(n) = 1+A277808(n).