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

2,1

Links

Table of n, a(n) for n=2..89.

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A000079, A003992.

Sequence in context: A343911 A125688 A230257 * A029404 A029417 A029237

Adjacent sequences: A060505 A060506 A060507 * A060509 A060510 A060511

Keyword

easy,nonn

Author

Labos Elemer, Apr 11 2001

Status

approved