A234810 Primes p such that p^2 divides 14^(p-1) - 1.

29, 353, 7596952219

Offset

1,1

Comments

Base 14 Wieferich primes.

Links

Table of n, a(n) for n=1..3.

Amir Akbary and Sahar Siavashi, The Largest Known Wieferich Numbers, INTEGERS, 18(2018), A3. See Table 1 p. 5.

Petr Ležák, Solutions of equation a^(p-1) mod p^2 = 1, p is prime

P. L. Montgomery, New solutions of a^p-1 == 1 (mod p^2), Math. Comp., 61 (203), 361-363

Mathematica

Select[Prime[Range[200]], Divisible[14^(# - 1) - 1, #^2] &] (* Alonso del Arte, Apr 20 2014 *)
Select[Prime[Range[200]], PowerMod[14, #-1, #^2]==1&] (* The program generates the first two terms of the sequence. To generate the third term, increase the Range constant to 351*10^5, but the program will take a long time to run. *) (* Harvey P. Dale, Jun 19 2021 *)

Prog

(PARI)
N=10^9; default(primelimit, N);
forprime(n=2, N, if(Mod(14, n^2)^(n-1)==1, print1(n, ", ")));

Crossrefs

Cf. A001220.

Sequence in context: A156640 A239743 A022689 * A077516 A142278 A281059

Adjacent sequences: A234807 A234808 A234809 * A234811 A234812 A234813

Keyword

nonn,hard,bref,more

Author

Felix Fröhlich, Apr 19 2014

Status

approved