A357362 Primes q such that either p^(q-1) == 1 (mod q^2) or q^(p-1) == 1 (mod p^2), where p = A151799(q).

7, 53, 59, 151057, 240733, 911135857

Offset: 1

Author

Felix Fröhlich, Sep 25 2022

Keywords

• nonn
• hard
• more

Crossrefs

Cf. A151799, A151800, A357363, A357364, A357365.

Programs

PARI

is(n) = my(b=precprime(n-1)); Mod(b, n^2)^(n-1)==1 || Mod(n, b^2)^(b-1)==1
forprime(p=3, , if(is(p), print1(p, ", ")))

Python

from sympy import nextprime
from itertools import islice
def agen():
    p, q = 2, 3
    while True:
        if pow(p, q-1, q*q) == 1 or pow(q, p-1, p*p) == 1: yield q
        p, q = q, nextprime(q)
print(list(islice(agen(), 5))) # Michael S. Branicky, Sep 30 2022

Extensions

a(6) from Michael S. Branicky, Sep 26 2022