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

%I #4 Oct 11 2017 09:15:26

%S 3,5,11,22,43,87,174,348,696,1392,2784,5567,11134,22268,44536,89073,

%T 178145,356291,712581,1425163,2850325,5700650,11401300,22802601,

%U 45605201,91210403,182420806,364841611,729683222,1459366444,2918732889,5837465777,11674931555

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

%H Clark Kimberling, <a href="/A293338/b293338.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) = A027437(n) if (fractional part of e*2^n) < 1/2, else a(n) = A293337(n).

%t z = 120; r = E;

%t Table[Floor[r*2^n], {n, 0, z}]; (* A027437 *)

%t Table[Ceiling[r*2^n], {n, 0, z}]; (* A293337 *)

%t Table[Round[r*2^n], {n, 0, z}]; (* A293338 *)

%Y Cf. A001113, A027437, A293337, A293341.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Oct 10 2017