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a(n) is the integer k that minimizes |e - k/Fibonacci(n)|.
3

%I #12 Feb 17 2018 12:23:01

%S 0,3,3,5,8,14,22,35,57,92,150,242,391,633,1025,1658,2683,4341,7024,

%T 11365,18389,29754,48143,77898,126041,203939,329980,533919,863900,

%U 1397819,2261719,3659539,5921258,9580796,15502054,25082850,40584905,65667755,106252660

%N a(n) is the integer k that minimizes |e - k/Fibonacci(n)|.

%H Clark Kimberling, <a href="/A293676/b293676.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) = A293674(n) if (fractional part of e*Fibonacci(n)) < 1/2, otherwise a(n) = A293675(n).

%t z = 120; f[n_] := Fibonacci[n];

%t Table[Floor[E*f[n]], {n, 0, z}]; (* A293674 *)

%t Table[Ceiling[E*f[n]], {n, 0, z}]; (* A293675 *)

%t Table[Round[E*f[n]], {n, 0, z}]; (* A293676 *)

%Y Cf. A001113, A293674, A293675.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Oct 16 2017