A067850 Highest power of 2 not exceeding n!.

0, 0, 1, 2, 4, 6, 9, 12, 15, 18, 21, 25, 28, 32, 36, 40, 44, 48, 52, 56, 61, 65, 69, 74, 79, 83, 88, 93, 97, 102, 107, 112, 117, 122, 127, 132, 138, 143, 148, 153, 159, 164, 169, 175, 180, 186, 191, 197, 202, 208, 214, 219, 225, 231, 237, 242, 248, 254, 260, 266

Offset: 0

Author

Lekraj Beedassy, Feb 15 2002

Keywords

• nonn

Comments

2^a(n) <= n! < 2^[a(n)+1]

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000142.

Cf. A003070 (minimum number of bits to represent n!)

Programs

Magma

[Floor(Log(2,Factorial(k))):k in [0..60]]; // Marius A. Burtea, Nov 06 2019

Mathematica

f[n_] := Block[{k = 0}, While[2^k <= n!, k++ ]; k--; k]; Table[ f[n], {n, 0, 60} ]

Formula

floor(log[2](n!)). - Vladeta Jovovic, Feb 18 2002

Extensions

Edited and extended by Robert G. Wilson v, Feb 16 2002