A347165 Primes p such that 2*p-1 and (2*p-1)^2+(2*p)^2 are also prime.

3, 79, 379, 829, 1279, 2029, 3019, 3109, 3529, 3709, 5479, 5749, 6379, 6709, 7219, 7369, 8689, 11839, 12049, 13219, 13729, 14029, 14419, 15319, 15349, 16189, 17659, 18229, 18439, 20809, 24979, 25819, 26539, 28549, 30859, 32119, 32359, 32779, 33739, 34729, 37039, 38569, 39079, 39679, 44119, 44449

Offset

1,1

Comments

Except for 3, all terms end in 9.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 379 is a term because 379, 2*379-1 = 757 and (2*379-1)^2+(2*379)^2 = 1147613 are prime.

Maple

filter:= proc(p) isprime(p) and isprime(2*p-1) and isprime(8*p^2-4*p+1) end proc:
select(filter, [3, seq(i, i=9..50000, 10)]);

Prog

(Python)
from sympy import isprime, primerange
def ok(p): return isprime(2*p-1) and isprime((2*p-1)**2 + (2*p)**2)
def aupto(limit): return list(filter(ok, primerange(2, limit+1)))
print(aupto(44450)) # Michael S. Branicky, Aug 20 2021

Crossrefs

Cf. A347110.

Sequence in context: A236069 A364947 A064456 * A073176 A236574 A367249

Adjacent sequences: A347162 A347163 A347164 * A347166 A347167 A347168

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Aug 20 2021

Status

approved