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Primes p such that p - 3 divides 3^p - 3.
2

%I #14 Apr 06 2021 02:58:04

%S 2,5,7,11,13,31,73,241,367,491,577,733,757,971,991,2593,2731,3307,

%T 3391,3529,4591,5113,7591,8011,8713,11131,17377,17911,18433,21757,

%U 24181,34651,36559,38921,39367,41141,52951,53593,55201,55681,59051,85933,93871,95791,102241,105031

%N Primes p such that p - 3 divides 3^p - 3.

%C Conjecture: the sequence is infinite.

%H Amiram Eldar, <a href="/A302988/b302988.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Prime[Range[25]], Divisible[3^# - 3, # - 3] &] (* _Alonso del Arte_, Apr 17 2018 *)

%t Select[Range[10^5], # != 3 && PrimeQ[#] && PowerMod[3, #, # - 3] == Mod[3, # - 3] &] (* _Amiram Eldar_, Apr 06 2021 *)

%o (PARI) isok(p) = isprime(p) && (p != 3) && (Mod(3,p-3)^p == Mod(3,p-3)); \\ _Michel Marcus_, Apr 17 2018

%Y Cf. A000040, A000244, A302987.

%K nonn

%O 1,1

%A _Alex Ratushnyak_, Apr 17 2018