OFFSET
1,1
COMMENTS
If prime p divides 3^k-2 and 5^k-1, then p divides 3^j-2 and 5^j-1 for all j such that j == k (mod p-1).
Primes p such that the equation 3^(x*A070677(p)) == 2 (mod p) has a solution.
Values of k: 24, 108, 64, 376020, 67141466, 487515840, ... - Chai Wah Wu, Feb 24 2023
EXAMPLE
a(3) = 2593 is a term because 2593 is prime, 3^64 == 2 (mod 2593) and 5^64 == 1 (mod 2593).
MAPLE
R:= NULL: count:= 0: p:= 5: with(numtheory):
while count < 4 do
p:= nextprime(p);
if mlog(2, 3 &^ order(5, p) mod p, p) <> FAIL then R:= R, p; count:= count+1 fi
od:
R;
PROG
(Python)
from itertools import islice
from sympy import discrete_log, nextprime, n_order
def A360761_gen(): # generator of terms
p = 5
while True:
try:
discrete_log(p:=nextprime(p), 2, pow(3, n_order(5, p), p))
except:
continue
yield p
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Robert Israel, Feb 19 2023
EXTENSIONS
a(5)-a(6) from Chai Wah Wu, Feb 23 2023
STATUS
approved