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A293402 The integer k that minimizes |k/n^2 - tau|, where tau = (1+sqrt(5))/2 (golden ratio).

%I A293402 #4 Oct 11 2017 18:14:51
%S A293402 0,2,6,15,26,40,58,79,104,131,162,196,233,273,317,364,414,468,524,584,
%T A293402 647,714,783,856,932,1011,1094,1180,1269,1361,1456,1555,1657,1762,
%U A293402 1870,1982,2097,2215,2336,2461,2589
%N A293402 The integer k that minimizes |k/n^2 - tau|, where tau = (1+sqrt(5))/2 (golden ratio).
%H A293402 Clark Kimberling, <a href="/A293402/b293402.txt">Table of n, a(n) for n = 0..1000</a>
%F A293402 a(n) = floor(1/2 + tau*n^2).
%F A293402 a(n) = A293400(n) if (fractional part of tau*n^2) < 1/2, else a(n) = A293401(n).
%t A293402 z = 120; r = GoldenRatio;
%t A293402 Table[Floor[r*n^2], {n, 0, z}];   (* A293400 *)
%t A293402 Table[Ceiling[r*n^2], {n, 0, z}]; (* A293401 *)
%t A293402 Table[Round[r*n^2], {n, 0, z}];   (* A293402 *)
%Y A293402 Cf. A001622, A293400, A293401.
%K A293402 nonn,easy
%O A293402 0,2
%A A293402 _Clark Kimberling_, Oct 11 2017