A357365 Primes q such that either p^(q-1) == 1 (mod q^2) or q^(p-1) == 1 (mod p^2), where p = A151799(A151799(A151799(A151799(q)))).

19, 67, 349, 2011, 22307, 13699249, 2018905087, 9809844767

Offset: 1

Author

Felix Fröhlich, Sep 25 2022

Keywords

• nonn
• hard
• more

Crossrefs

Cf. A151799, A151800, A357362, A357363, A357364.

Programs

PARI

is(n) = my(b=precprime(precprime(precprime(precprime(n-1)-1)-1)-1)); Mod(b, n^2)^(n-1)==1 || Mod(n, b^2)^(b-1)==1
forprime(p=11, , if(is(p), print1(p, ", ")))

Python

from sympy import nextprime
from itertools import islice
def agen():
    p, m1, m2, m3, q = 2, 3, 5, 7, 11
    while True:
        if pow(p, q-1, q*q) == 1 or pow(q, p-1, p*p) == 1: yield q
        p, m1, m2, m3, q = m1, m2, m3, q, nextprime(q)
print(list(islice(agen(), 5))) # Michael S. Branicky, Sep 30 2022

Extensions

a(7)-a(8) from Michael S. Branicky, Sep 26 2022