A293404 Least integer k such that k/n^2 > (3 + sqrt(5))/2 (the golden ratio).

0, 3, 11, 24, 42, 66, 95, 129, 168, 213, 262, 317, 377, 443, 514, 590, 671, 757, 849, 946, 1048, 1155, 1268, 1385, 1508, 1637, 1770, 1909, 2053, 2202, 2357, 2516, 2681, 2852, 3027, 3208, 3393, 3585, 3781, 3983, 4189, 4401, 4619, 4841, 5069, 5302, 5540, 5784

Offset: 0

Author

Clark Kimberling, Oct 11 2017

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A001622, A293402, A293403, A293405.

Programs

Mathematica

z = 120; r = 1+GoldenRatio;
Table[Floor[r*n^2], {n, 0, z}];   (* A293403 *)
Table[Ceiling[r*n^2], {n, 0, z}]; (* A293404 *)
Table[Round[r*n^2], {n, 0, z}];   (* A293405 *)

Formula

a(n) = ceiling(r*n^2), where r = (3 + sqrt(5))/2.

a(n) = A293403(n) + 1 for n > 0.