A293400 Greatest integer k such that k/n^2 < (1 + sqrt(5))/2 (the golden ratio).

0, 1, 6, 14, 25, 40, 58, 79, 103, 131, 161, 195, 232, 273, 317, 364, 414, 467, 524, 584, 647, 713, 783, 855, 931, 1011, 1093, 1179, 1268, 1360, 1456, 1554, 1656, 1762, 1870, 1982, 2096, 2215, 2336, 2461, 2588

Offset: 0

Author

Clark Kimberling, Oct 11 2017

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000
• Felipe Gonçalves, Diogo Oliveira e Silva, João P. G. Ramos, New Sign Uncertainty Principles, arXiv:2003.10771 [math.CA], 2020.

Crossrefs

Cf. A001622, A293401, A293402.

Programs

Magma

[Floor((1 + Sqrt(5))/2*n^2) : n in [0..80]]; // Wesley Ivan Hurt, Jul 03 2020

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 *)

Formula

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

a(n) = A293401(n) - 1 for n > 0.