A293420 - OEIS

%I #12 Sep 08 2022 08:46:19

%S 0,1,1,3,4,7,11,18,30,48,78,126,204,330,533,863,1396,2258,3654,5913,

%T 9567,15480,25047,40527,65574,106101,171676,277777,449453,727230,

%U 1176682,1903912,3080594,4984506,8065100,13049606,21114706,34164312,55279019,89443331

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

%H Clark Kimberling, <a href="/A293420/b293420.txt">Table of n, a(n) for n = 0..1000</a>

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

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

%t z = 120; r = Sqrt[2]; f[n_] := Fibonacci[n];

%t Table[Floor[r*f[n]], {n, 0, z}];   (* A293418 *)

%t Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293419 *)

%t Table[Round[r*f[n]], {n, 0, z}];   (* A293420 *)

%o (PARI) for(n=0,30, print1(round(fibonacci(n)*sqrt(2)), ", ")) \\ _G. C. Greubel_, Feb 08 2018

%o (Magma) [Round(Fibonacci(n)*Sqrt(2)): n in [0..30]]; // _G. C. Greubel_, Feb 08 2018

%Y Cf. A000045, A293418, A293419.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Oct 12 2017