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

0,4

Comments

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

Links

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000142.

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

Sequence in context: A130664 A014011 A064424 * A130240 A143118 A162800

Adjacent sequences: A067847 A067848 A067849 * A067851 A067852 A067853

Keyword

nonn

Author

Lekraj Beedassy, Feb 15 2002

Extensions

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

Status

approved