A096385 - OEIS

%I #23 Apr 23 2022 14:45:57

%S 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,

%T 13,59,11,311,3,67,67,71,5,149,37,61,3,83,5,173,23,31,47,283,5,29,11,

%U 103,5,107,5,31,13,7,59,709,7,367,61,37,3,131,23,269,13,139,29,569

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

%H Harvey P. Dale, <a href="/A096385/b096385.txt">Table of n, a(n) for n = 2..1000</a>

%e 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.

%t 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 *)

%o (PARI) a(n) = my(p=2); while (Mod(p,n)^n !=1, p=nextprime(p+1)); p; \\ _Michel Marcus_, Feb 07 2021

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

%K nonn

%O 2,1

%A _Reinhard Zumkeller_, Aug 05 2004