A355545 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.

1093, 3511, 20771, 1006003, 1747591, 5395561, 53471161

Offset

1,1

Links

Table of n, a(n) for n=1..7.

Example

p = 1747591 satisfies 13^(p-1) == 1 (mod p^2) and 13 is a factor of 1747590, so 1747591 is a term of the sequence.

Prog

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

Crossrefs

Cf. A355546.

Sequence in context: A291961 A001220 A265630 * A291194 A331021 A270833

Adjacent sequences: A355542 A355543 A355544 * A355546 A355547 A355548

Keyword

nonn,hard,more

Author

Felix Fröhlich, Jul 06 2022

Status

approved