A293679 a(n) is the integer k that minimizes |k/Fibonacci(n) - Pi|.

0, 3, 3, 6, 9, 16, 25, 41, 66, 107, 173, 280, 452, 732, 1184, 1916, 3101, 5017, 8118, 13135, 21253, 34388, 55641, 90029, 145669, 235698, 381367, 617065, 998433, 1615498, 2613931, 4229429, 6843360, 11072788, 17916148, 28988936, 46905084, 75894020, 122799105

Offset: 0

Author

Clark Kimberling, Oct 16 2017

Keywords

• nonn
• easy
• base

Links

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

Crossrefs

Cf. A000045, A000796, A293677, A293678.

Programs

Mathematica

z = 120; f[n_] := Fibonacci[n];
Table[Floor[Pi*f[n]], {n, 0, z}];   (* A293677 *)
Table[Ceiling[Pi*f[n]], {n, 0, z}]; (* A293678 *)
Table[Round[Pi*f[n]], {n, 0, z}];   (* A293679 *)

Formula

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

a(n) = A293677(n) if (fractional part of Pi*Fibonacci(n)) < 1/2, otherwise a(n) = A293678(n).