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

%I A293679 #14 Feb 17 2018 12:23:38
%S A293679 0,3,3,6,9,16,25,41,66,107,173,280,452,732,1184,1916,3101,5017,8118,
%T A293679 13135,21253,34388,55641,90029,145669,235698,381367,617065,998433,
%U A293679 1615498,2613931,4229429,6843360,11072788,17916148,28988936,46905084,75894020,122799105
%N A293679 a(n) is the integer k that minimizes |k/Fibonacci(n) - Pi|.
%H A293679 Clark Kimberling, <a href="/A293679/b293679.txt">Table of n, a(n) for n = 0..1000</a>
%F A293679 a(n) = floor(1/2 + Pi*Fibonacci(n)).
%F A293679 a(n) = A293677(n) if (fractional part of Pi*Fibonacci(n)) < 1/2, otherwise a(n) = A293678(n).
%t A293679 z = 120; f[n_] := Fibonacci[n];
%t A293679 Table[Floor[Pi*f[n]], {n, 0, z}];   (* A293677 *)
%t A293679 Table[Ceiling[Pi*f[n]], {n, 0, z}]; (* A293678 *)
%t A293679 Table[Round[Pi*f[n]], {n, 0, z}];   (* A293679 *)
%Y A293679 Cf. A000045, A000796, A293677, A293678.
%K A293679 nonn,easy,base
%O A293679 0,2
%A A293679 _Clark Kimberling_, Oct 16 2017