A293407 - OEIS

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

%S 0,1,3,6,10,16,23,31,40,51,62,75,89,105,122,140,159,179,201,224,248,

%T 273,300,327,356,387,418,451,485,520,557,594,633,674,715,758,801,847,

%U 893,941,989,1039,1091,1143,1197,1252,1308,1366,1424,1484,1546,1608,1672

%N Least integer k such that k/n^2 > (-1 + sqrt(5))/2 (the golden ratio).

%H Clark Kimberling, <a href="/A293407/b293407.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = ceiling(r*n^2), where r = (-1 + sqrt(5))/2.

%F a(n) = A152738(n) + 1 for n > 0.

%t z = 120; r = -1+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, A293401, A293403, A152738, A293408.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Oct 11 2017