A198020 Number of distinct residues of x^n (mod 2n+1), x=0..2n.

1, 3, 3, 3, 4, 3, 3, 15, 3, 3, 8, 3, 6, 19, 3, 3, 12, 35, 3, 39, 3, 3, 12, 3, 8, 51, 3, 55, 20, 3, 3, 49, 8, 3, 24, 3, 3, 63, 24, 3, 28, 3, 27, 87, 3, 15, 32, 95, 3, 77, 3, 3, 16, 3, 3, 111, 3, 115, 28, 119, 12, 123, 51, 3, 44, 3, 8, 95, 3, 3, 48, 143, 16, 129

Offset: 0

Author

Michel Lagneau, Oct 20 2011

Keywords

• nonn

Comments

a(n) = 3 if 2n+1 prime because the corresponding residues are 0, 1 and 2n (mod 2n+1).

Examples

			a(7) = 15 because x^7  == 0, 1, …,14  (mod 15) => 15 distinct residues.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A195637, A197929.

Programs

Mathematica

Table[Length[Union[PowerMod[Range[0, 2*n], n, 2*n+1]]], {n,0, 100}]