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%I #13 Sep 08 2022 08:46:19
%S 0,2,2,3,5,8,12,19,30,49,78,126,204,330,534,863,1396,2259,3655,5913,
%T 9568,15480,25048,40528,65575,106102,171676,277777,449453,727230,
%U 1176683,1903912,3080595,4984507,8065101,13049607,21114707,34164313,55279019,89443332
%N a(n) is the least integer k such that k/Fibonacci(n) > sqrt(2).
%H Clark Kimberling, <a href="/A293419/b293419.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = ceiling(Fibonacci(n)*sqrt(2)).
%F a(n) = A293418(n) + 1 for n > 0.
%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(ceil(fibonacci(n)*sqrt(2)), ", ")) \\ _G. C. Greubel_, Feb 08 2018
%o (Magma) [Ceiling(Fibonacci(n)*Sqrt(2)): n in [0..30]]; // _G. C. Greubel_, Feb 08 2018
%Y Cf. A000045, A293418, A293420.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Oct 12 2017
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