A293408 - OEIS

%I #4 Oct 11 2017 21:57:18

%S 0,1,2,6,10,15,22,30,40,50,62,75,89,104,121,139,158,179,200,223,247,

%T 273,299,327,356,386,418,451,485,520,556,594,633,673,714,757,801,846,

%U 892,940,989,1039,1090,1143,1197,1252,1308,1365,1424,1484,1545,1608,1671

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

%H Clark Kimberling, <a href="/A293408/b293408.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = floor(1/2 + (n^2)/tau).

%F a(n) = A152738(n) if (fractional part of (1/tau)*n^2) < 1/2, else a(n) = A293407(n).

%t z = 120; r = -11+GoldenRatio;

%t Table[Floor[r*n^2], {n, 0, z}];   (* A152738 *)

%t Table[Ceiling[r*n^2], {n, 0, z}]; (* A293407 *)

%t Table[Round[r*n^2], {n, 0, z}];   (* A293408 *)

%Y Cf. A001622, A293402, A293404, A152738, A293407.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Oct 11 2017