A342831 a(n) is the smallest positive integer k such that the n-dimensional cube [0,k]^n contains at least as many internal lattice points as external lattice points.

3, 6, 9, 12, 15, 18, 21, 24, 26, 29, 32, 35, 38, 41, 44, 47, 50, 52, 55, 58, 61, 64, 67, 70, 73, 76, 78, 81, 84, 87, 90, 93, 96, 99, 101, 104, 107, 110, 113, 116, 119, 122, 125, 127, 130, 133, 136, 139, 142, 145, 148, 151, 153, 156, 159, 162, 165, 168, 171, 174, 177, 179, 182

Offset: 1

Author

Gary Yane, Mar 23 2021

Keywords

• nonn

Examples

			a(2) > 5 because the number of internal lattice points = 4^2 = 16 < 20 = 6^2 - 16 = the number of external lattice points, therefore a(2)=6 because the number of internal lattice points = 5^2 = 25 > 24 = 7^2 - 25 = number of external lattice points.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A078608.

Programs

Maple

a:= n-> ceil(1+2/(2^(1/n)-1)):
seq(a(n), n=1..65);  # Alois P. Heinz, Apr 20 2021

Mathematica

a[1] = 3; a[n_] := Floor[2^(1/n + 1)/(2^(1/n) - 1)]; Array[a, 100] (* Amiram Eldar, Mar 31 2021 *)

Formula

a(1) = 3 and a(n) = floor(2^(1/n+1)/(2^(1/n)-1)) for n > 1.

a(n) = A078608(n) + 1.