A293362 Greatest integer k such that k/2^n < log 2.

0, 1, 2, 5, 11, 22, 44, 88, 177, 354, 709, 1419, 2839, 5678, 11356, 22713, 45426, 90852, 181704, 363408, 726817, 1453634, 2907269, 5814539, 11629079, 23258159, 46516319, 93032639, 186065279, 372130558, 744261117, 1488522235, 2977044471, 5954088943

Offset

0,3

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Formula

a(n) = floor(r*2^n), where r = log 2.

a(n) = A293363(n) - 1.

From Greg Huber, Feb 13 2019: (Start)

a(n) = nearest integer to the integral dx/sin(x) from Pi/(2^(2^n)) to Pi/2.

a(n) = nearest integer to -log(tan(Pi/(2^(2^n+1)))) (follows from the integral formula). (End)

Mathematica

z = 120; r = Log[2];
Table[Floor[r*2^n], {n, 0, z}];   (* A293362 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293363 *)
Table[Round[r*2^n], {n, 0, z}];   (* A293364 *)

Prog

(PARI) {a(n) = (log(2)*2^n)\1 }; \\ G. C. Greubel, Feb 13 2019
(Magma) [Floor(Log(2)*2^n): n in [0..40]]; // G. C. Greubel, Feb 13 2019
(Sage) [floor(log(2)*2^n) for n in range(40)] # G. C. Greubel, Feb 13 2019

Crossrefs

Cf. A002162, A293363, A293364.

Sequence in context: A352045 A351970 A071015 * A362583 A084188 A266721

Adjacent sequences: A293359 A293360 A293361 * A293363 A293364 A293365

Keyword

nonn,easy

Author

Clark Kimberling, Oct 11 2017

Status

approved