cp's OEIS Frontend

A352604 Primes p such that p^2+3*p+1 and p^2+p-1 are also prime.

%I A352604 #10 Mar 23 2022 18:40:14
%S A352604 2,3,5,19,53,59,163,263,349,373,419,449,499,1013,1093,1259,1303,1423,
%T A352604 1489,1493,1669,1759,2069,2729,2879,3463,3943,4159,4243,4283,4493,
%U A352604 4603,4793,4969,5113,5303,5563,6323,6599,6803,6829,6883,7369,7523,7529,7963,8039,8713,8969,9043,9173,9293,9623
%N A352604 Primes p such that p^2+3*p+1 and p^2+p-1 are also prime.
%C A352604 Primes p such that (p-1)*p+(p-1)+p and p*(p+1)+p+(p+1) are also prime.
%H A352604 Robert Israel, <a href="/A352604/b352604.txt">Table of n, a(n) for n = 1..10000</a>
%e A352604 a(3) = 5 is a term because 5, 5^2+3*5+1 = 41 and 5^2+5-1 = 29 are all prime.
%p A352604 select(t -> isprime(t^2+3*t+1) and isprime(t^2+t-1), [seq(ithprime(i),i=1..10000)]);
%o A352604 (Python)
%o A352604 from itertools import islice
%o A352604 from sympy import isprime, nextprime
%o A352604 def agen():
%o A352604     p = 2
%o A352604     while True:
%o A352604         if isprime(p**2 + 3*p + 1) and isprime(p**2 + p - 1):
%o A352604             yield p
%o A352604         p = nextprime(p)
%o A352604 print(list(islice(agen(), 53))) # _Michael S. Branicky_, Mar 22 2022
%Y A352604 Intersection of A053184 and A153590.
%K A352604 nonn
%O A352604 1,1
%A A352604 _J. M. Bergot_ and _Robert Israel_, Mar 22 2022