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A293362 Greatest integer k such that k/2^n < log 2. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
Sequence in context: A352045 A351970 A071015 * A362583 A084188 A266721
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 11 2017
STATUS
approved

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Last modified April 13 05:19 EDT 2024. Contains 371639 sequences. (Running on oeis4.)