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
Keywords
Examples
a(3) = 379 is a term because 379, 2*379-1 = 757 and (2*379-1)^2+(2*379)^2 = 1147613 are prime.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A347110.
Programs
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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)]);
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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
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