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

1,1

Links

Table of n, a(n) for n=1..6.

Prog

(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

Crossrefs

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

Sequence in context: A300932 A300875 A301485 * A224501 A241487 A236688

Adjacent sequences: A357359 A357360 A357361 * A357363 A357364 A357365

Keyword

nonn,hard,more

Author

Felix Fröhlich, Sep 25 2022

Extensions

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

Status

approved