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

1,1

Links

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

Formula

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

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

Example

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.

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 *)

Crossrefs

Cf. A078608.

Sequence in context: A160943 A160930 A212662 * A161351 A328168 A209258

Adjacent sequences: A342828 A342829 A342830 * A342832 A342833 A342834

Keyword

nonn

Author

Gary Yane, Mar 23 2021

Status

approved