A293362 - OEIS

%I #15 Sep 08 2022 08:46:19

%S 0,1,2,5,11,22,44,88,177,354,709,1419,2839,5678,11356,22713,45426,

%T 90852,181704,363408,726817,1453634,2907269,5814539,11629079,23258159,

%U 46516319,93032639,186065279,372130558,744261117,1488522235,2977044471,5954088943

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

%H Clark Kimberling, <a href="/A293362/b293362.txt">Table of n, a(n) for n = 0..1000</a>

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

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

%F From _Greg Huber_, Feb 13 2019: (Start)

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

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

%t z = 120; r = Log[2];

%t Table[Floor[r*2^n], {n, 0, z}];   (* A293362 *)

%t Table[Ceiling[r*2^n], {n, 0, z}]; (* A293363 *)

%t Table[Round[r*2^n], {n, 0, z}];   (* A293364 *)

%o (PARI) {a(n) = (log(2)*2^n)\1 }; \\ _G. C. Greubel_, Feb 13 2019

%o (Magma) [Floor(Log(2)*2^n): n in [0..40]]; // _G. C. Greubel_, Feb 13 2019

%o (Sage) [floor(log(2)*2^n) for n in range(40)] # _G. C. Greubel_, Feb 13 2019

%Y Cf. A002162, A293363, A293364.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Oct 11 2017