A355546 - OEIS

%I #10 Jul 10 2022 16:07:27

%S 11,1093,3511,7195291,11642831,13703077,112955593,5857727461

%N Primes p that satisfy q^(p-1) == 1 (mod p^2), i.e., are base-q Wieferich primes, for a prime q dividing p+1.

%e p = 7195291 satisfies 138371^(p-1) == 1 (mod p^2) and 138371 is a factor of 7195292, so 7195291 is a term of the sequence.

%o (PARI) is(n) = my(f=factor(n+1)[, 1]~); for(k=1, #f, if(Mod(f[k], n^2)^(n-1)==1, return(1))); 0

%o forprime(p=1, , if(is(p), print1(p, ", ")))

%Y Cf. A355545.

%K nonn,hard,more

%O 1,1

%A _Felix Fröhlich_, Jul 06 2022

%E a(8) from _Michael S. Branicky_, Jul 10 2022