A096385 a(n) = smallest prime p with p^n mod n = 1.

3, 7, 3, 11, 5, 29, 3, 7, 11, 23, 5, 53, 13, 31, 3, 103, 5, 191, 3, 37, 23, 47, 5, 11, 53, 7, 13, 59, 11, 311, 3, 67, 67, 71, 5, 149, 37, 61, 3, 83, 5, 173, 23, 31, 47, 283, 5, 29, 11, 103, 5, 107, 5, 31, 13, 7, 59, 709, 7, 367, 61, 37, 3, 131, 23, 269, 13, 139, 29, 569

Offset: 2

Author

Reinhard Zumkeller, Aug 05 2004

Keywords

• nonn

Examples

			n=5: 2^5=32=5*6+2, 3^5=243=5*48+3, 5^5 mod 5 = 0, 7^5=16807=5*3361+2, 11^5=161051=5*32210+1: a(5)=11.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A015910, A066601, A066603, A066438, A066441.

Programs

Mathematica

With[{prs=Prime[Range[200]]},Table[SelectFirst[prs,PowerMod[#,n,n]==1&],{n,2,80}]] (* The program uses the SelectFirst function from Mathematica version 10 *) (* Harvey P. Dale, Aug 31 2015 *)

PARI

a(n) = my(p=2); while (Mod(p,n)^n !=1, p=nextprime(p+1)); p; \\ Michel Marcus, Feb 07 2021