A099396 a(n) = floor(log_2((2/3)*n)) for n >= 2, a(1) = 0.

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

Offset: 1

Author

Ralf Stephan, Oct 21 2004

Keywords

• nonn
• easy

Crossrefs

First differences are in A099395. Cf. A004762, A007283.

Programs

Maple

0, seq(ilog2(2/3*n), n=2..110); # Georg Fischer, Aug 31 2021

Mathematica

Join[{0},Floor[Log[2,2/3 Range[2,110]]]] (* Harvey P. Dale, Mar 01 2012 *)

PARI

a(n) = if(n == 1, 0, my(L = logint(n, 2)); L + bittest(n, L-1) - 1) \\ Mikhail Kurkov, Mar 13 2024

Formula

G.f.: (1/(1-x)) * Sum_{k>=0} x^(3*2^k).

Extensions

Definition corrected by Georg Fischer, Aug 31 2021