A293361 The integer k that minimizes |k/2^n - e^2|.

7, 15, 30, 59, 118, 236, 473, 946, 1892, 3783, 7566, 15133, 30266, 60531, 121062, 242125, 484249, 968498, 1936997, 3873993, 7747987, 15495974, 30991948, 61983895, 123967790, 247935580, 495871161, 991742322, 1983484643, 3966969287, 7933938573, 15867877147

Offset: 0

Author

Clark Kimberling, Oct 11 2017

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A072334, A293359, A293360.

Programs

Mathematica

z = 120; r = E^2;
Table[Floor[r*2^n], {n, 0, z}];   (* A293359 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293360 *)
Table[Round[r*2^n], {n, 0, z}];   (* A293361 *)

Formula

a(n) = floor(1/2 + (e^2)*2^n).

a(n) = A293359(n) if (fractional part of (e^2)*2^n) < 1/2, else a(n) = A293360(n).