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A293408 The integer k that minimizes |k/n^2 - 1/tau|, where tau = (1+sqrt(5))/2 (golden ratio).

%I A293408 #4 Oct 11 2017 21:57:18
%S A293408 0,1,2,6,10,15,22,30,40,50,62,75,89,104,121,139,158,179,200,223,247,
%T A293408 273,299,327,356,386,418,451,485,520,556,594,633,673,714,757,801,846,
%U A293408 892,940,989,1039,1090,1143,1197,1252,1308,1365,1424,1484,1545,1608,1671
%N A293408 The integer k that minimizes |k/n^2 - 1/tau|, where tau = (1+sqrt(5))/2 (golden ratio).
%H A293408 Clark Kimberling, <a href="/A293408/b293408.txt">Table of n, a(n) for n = 0..1000</a>
%F A293408 a(n) = floor(1/2 + (n^2)/tau).
%F A293408 a(n) = A152738(n) if (fractional part of (1/tau)*n^2) < 1/2, else a(n) = A293407(n).
%t A293408 z = 120; r = -11+GoldenRatio;
%t A293408 Table[Floor[r*n^2], {n, 0, z}];   (* A152738 *)
%t A293408 Table[Ceiling[r*n^2], {n, 0, z}]; (* A293407 *)
%t A293408 Table[Round[r*n^2], {n, 0, z}];   (* A293408 *)
%Y A293408 Cf. A001622, A293402, A293404, A152738, A293407.
%K A293408 nonn,easy
%O A293408 0,3
%A A293408 _Clark Kimberling_, Oct 11 2017