A060508 Exponent of largest power of n < 2^n.

2, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13

Offset: 2

Author

Labos Elemer, Apr 11 2001

Keywords

• easy
• nonn

Examples

			For n = 10, 1000 < 1024 < 10000, so a(10) = 3; a(1) is indeterminate, since 1^j < 2^1.
		

Crossrefs

Cf. A000079, A003992.

Programs

Mathematica

Table[Floor[n/Log[2, n]],{n,2,89}] (* Stefano Spezia, Dec 07 2021 *)

Formula

a(n) = floor(n/log(2, n)); n^a(n) <= 2^n <= n^(1+a(n)).