%I #19 May 17 2019 14:43:23

%S 5,7,37,331,33923,1284043

%N Primes p such that p^2 divides 18^(p-1) - 1.

%C Base 18 Wieferich primes. According to Richard Fischer there is no other term up to approximately 5*10^13.

%H Amir Akbary and Sahar Siavashi, <a href="http://math.colgate.edu/~integers/s3/s3.Abstract.html">The Largest Known Wieferich Numbers</a>, INTEGERS, 18(2018), A3. See Table 1 p. 5.

%H R. Fischer, <a href="http://www.fermatquotient.com/FermatQuotienten/FermQ_Sort">Thema: Fermatquotient B^(P-1) == 1 (mod P^2)</a>

%t Select[Prime[Range[1000000]], PowerMod[18, # - 1, #^2] == 1 &] (* _Robert Price_, May 17 2019 *)

%o (PARI) forprime(n=2, 10^9, if(Mod(18, n^2)^(n-1)==1, print1(n, ", ")));

%Y Cf. A001220, A014127, A123692, A212583, A123693, A045616, A111027, A128667, A234810, A242741, A128668, A090968, A242982, A039951, A096082.

%K nonn,hard,more

%O 1,1

%A _Felix Fröhlich_, Jun 24 2014