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The integer k that minimizes |k/2^n - 1/e|.
4

%I #4 Oct 11 2017 09:15:49

%S 0,1,1,3,6,12,24,47,94,188,377,753,1507,3014,6027,12055,24109,48219,

%T 96437,192875,385750,771499,1542998,3085996,6171993,12343986,24687971,

%U 49375943,98751886,197503771,395007542,790015084,1580030169,3160060337,6320120675

%N The integer k that minimizes |k/2^n - 1/e|.

%H Clark Kimberling, <a href="/A293341/b293341.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) = A293339(n) if (fractional part of (1/e)*2^n) < 1/2, else a(n) = A293340(n).

%t z = 120; r = 1/E;

%t Table[Floor[r*2^n], {n, 0, z}]; (* A293339 *)

%t Table[Ceiling[r*2^n], {n, 0, z}]; (* A293340 *)

%t Table[Round[r*2^n], {n, 0, z}]; (* A293341 *)

%Y Cf. A001113, A027437, A293339, A293340.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Oct 10 2017