A293677 -id:A293677 - cp's OEIS frontend

A293678 a(n) is the least integer k such that k/Fibonacci(n) > Pi.

0, 4, 4, 7, 10, 16, 26, 41, 66, 107, 173, 280, 453, 732, 1185, 1917, 3101, 5018, 8118, 13135, 21253, 34388, 55641, 90029, 145670, 235698, 381368, 617066, 998433, 1615499, 2613931, 4229429, 6843360, 11072789, 17916148, 28988937, 46905085, 75894021, 122799105

Offset: 0

Clark Kimberling, Oct 16 2017

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

Cf. A000045, A000796, A293677, A293679.

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 *)

a(n) = ceiling(Pi*Fibonacci(n)).

a(n) = A293677(n) + 1 for n > 0.

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

Original entry on oeis.org

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

Clark Kimberling, Oct 16 2017

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

Cf. A000045, A000796, A293677, A293678.

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 *)

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).

cp's OEIS Frontend

A293678 a(n) is the least integer k such that k/Fibonacci(n) > Pi.

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