A293676 a(n) is the integer k that minimizes |e - k/Fibonacci(n)|.

0, 3, 3, 5, 8, 14, 22, 35, 57, 92, 150, 242, 391, 633, 1025, 1658, 2683, 4341, 7024, 11365, 18389, 29754, 48143, 77898, 126041, 203939, 329980, 533919, 863900, 1397819, 2261719, 3659539, 5921258, 9580796, 15502054, 25082850, 40584905, 65667755, 106252660

Offset

0,2

Links

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

Formula

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

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

Mathematica

z = 120; f[n_] := Fibonacci[n];
Table[Floor[E*f[n]], {n, 0, z}];   (* A293674 *)
Table[Ceiling[E*f[n]], {n, 0, z}]; (* A293675 *)
Table[Round[E*f[n]], {n, 0, z}];   (* A293676 *)

Crossrefs

Cf. A001113, A293674, A293675.

Sequence in context: A200741 A271970 A213678 * A303714 A098353 A073060

Adjacent sequences: A293673 A293674 A293675 * A293677 A293678 A293679

Keyword

nonn,easy

Author

Clark Kimberling, Oct 16 2017

Status

approved