A198033 Greatest residue of x^n (mod 2n+1), x=0..2n.

0, 2, 4, 6, 7, 10, 12, 14, 16, 18, 18, 22, 21, 26, 28, 30, 31, 34, 36, 38, 40, 42, 40, 46, 43, 50, 52, 54, 55, 58, 60, 62, 61, 66, 64, 70, 72, 74, 71, 78, 79, 82, 84, 86, 88, 90, 90, 94, 96, 98, 100, 102, 100, 106, 108, 110, 112, 114, 108, 118, 111, 122, 124

Offset: 0

Author

Michel Lagneau, Oct 20 2011

Keywords

• nonn

Comments

If 2n+1 is prime, a(n) = 2n. But there exists nonprime numbers of the form 2n+1 such that a(n) = 2n, for example n = 0, 7, 13, 17, 19, 25, 27, 31, 37, 42, …

Examples

			a(10) = 18 because x^10 == 0, 1, 4, 7, 9, 15, 16, 18 (mod 21) => 18 is the greatest residue.
		

Links

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

Crossrefs

Cf. A196082, A198020, A198032.

Programs

Mathematica

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