A293401 Least integer k such that k/n^2 > (1 + sqrt(5))/2 (the golden ratio).

0, 2, 7, 15, 26, 41, 59, 80, 104, 132, 162, 196, 233, 274, 318, 365, 415, 468, 525, 585, 648, 714, 784, 856, 932, 1012, 1094, 1180, 1269, 1361, 1457, 1555, 1657, 1763, 1871, 1983, 2097, 2216, 2337, 2462, 2589

Offset

0,2

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Formula

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

a(n) = A293400(n) + 1 for n > 0.

Mathematica

z = 120; r = GoldenRatio;
Table[Floor[r*n^2], {n, 0, z}];   (* A293400 *)
Table[Ceiling[r*n^2], {n, 0, z}]; (* A293401 *)
Table[Round[r*n^2], {n, 0, z}];   (* A293402 *)

Crossrefs

Cf. A001622, A293400, A293402.

Sequence in context: A029888 A194112 A005449 * A323038 A333637 A113422

Adjacent sequences: A293398 A293399 A293400 * A293402 A293403 A293404

Keyword

nonn,easy

Author

Clark Kimberling, Oct 11 2017

Status

approved