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

0,2

Links

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

Formula

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

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

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 *)

Crossrefs

Cf. A001622, A293402, A293403, A293405.

Sequence in context: A120088 A081737 A005475 * A293414 A212252 A295622

Adjacent sequences: A293401 A293402 A293403 * A293405 A293406 A293407

Keyword

nonn,easy

Author

Clark Kimberling, Oct 11 2017

Status

approved