A293410 Least integer k such that k/n^2 > sqrt(3).

0, 2, 7, 16, 28, 44, 63, 85, 111, 141, 174, 210, 250, 293, 340, 390, 444, 501, 562, 626, 693, 764, 839, 917, 998, 1083, 1171, 1263, 1358, 1457, 1559, 1665, 1774, 1887, 2003, 2122, 2245, 2372, 2502, 2635, 2772, 2912, 3056, 3203, 3354, 3508, 3666, 3827, 3991

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. A002194, A171972, A070169.

Programs

Mathematica

z = 120; r = Sqrt[3];
Table[Floor[r*n^2], {n, 0, z}];   (* A171972 *)
Table[Ceiling[r*n^2], {n, 0, z}]; (* A293410 *)
Table[Round[r*n^2], {n, 0, z}];   (* A070169 *)

Python

from math import isqrt
def A293410(n): return 1+isqrt(3*n**4-1) if n else 0 # Chai Wah Wu, Jul 31 2022

Formula

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

a(n) = A171972(n) + 1 for n > 0.