A004257 a(n) = round(log_2(n)).

0, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 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, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000523 (floored).

Programs

Magma

[Round(Log(2,n)):n in [1..90]]; // Marius A. Burtea, Aug 02 2019

Mathematica

Round[Log[2,Range[90]]] (* Harvey P. Dale, Aug 26 2014 *)

PARI

a(n) = round(log(n)/log(2)); \\ Michel Marcus, Dec 11 2016

PARI

a(n) = {logint(n^2,2) - logint(n,2)} \\ Andrew Howroyd, Sep 11 2019

Formula

a(n) = floor(log_2(sqrt(2)*n)). - Velin Yanev, Dec 11 2016

Conjecture: a(n) = A000523(n^2) - A000523(n). - Mikhail Kurkov, Sep 11 2019