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

1,3

Links

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000523 (floored).

Sequence in context: A227923 A346425 A029836 * A360010 A276611 A238598

Adjacent sequences: A004254 A004255 A004256 * A004258 A004259 A004260

Keyword

nonn

Author

N. J. A. Sloane

Status

approved