A293420 a(n) is the integer k that minimizes |k/Fibonacci(n) - sqrt(2)|.

0, 1, 1, 3, 4, 7, 11, 18, 30, 48, 78, 126, 204, 330, 533, 863, 1396, 2258, 3654, 5913, 9567, 15480, 25047, 40527, 65574, 106101, 171676, 277777, 449453, 727230, 1176682, 1903912, 3080594, 4984506, 8065100, 13049606, 21114706, 34164312, 55279019, 89443331

Offset: 0

Author

Clark Kimberling, Oct 12 2017

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000045, A293418, A293419.

Programs

Magma

[Round(Fibonacci(n)*Sqrt(2)): n in [0..30]]; // G. C. Greubel, Feb 08 2018

Mathematica

z = 120; r = Sqrt[2]; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 0, z}];   (* A293418 *)
Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293419 *)
Table[Round[r*f[n]], {n, 0, z}];   (* A293420 *)

PARI

for(n=0,30, print1(round(fibonacci(n)*sqrt(2)), ", ")) \\ G. C. Greubel, Feb 08 2018

Formula

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

a(n) = A293418(n) if (fractional part of Fibonacci(n)*sqrt(2)) < 1/2, otherwise a(n) = A293419(n).