A254044 a(1) = 1, for n>1: a(n) = a(A253889(n)) + (1 if n is of the form 3n or 3n+1, otherwise 0).

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

Offset: 1

Author

Antti Karttunen, Jan 23 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192

Crossrefs

Positions of ones: A007051.

Cf. A000120, A032766, A064216, A253889, A253894, A254045.

Formula

a(1) = 1, for n>1: a(n) = a(A253889(n)) + [n is of the form 3n or 3n+1, i.e., in A032766] (Here [ ] is Iverson bracket).

a(1) = 0, thereafter, if n = 3k+2, then a(n) = a((n+1)/3), otherwise a(n) = 1 + a(A253889(n)).

a(n) = A000120(A064216(n)). [Binary weight of terms of A064216.]

a(n) = A253894(n) - A254045(n).

Other identities:

a(A007051(n)) = 1 for all n >= 0. [And no 1's in any other positions.]