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Primes p such that prime(p) + 2*p^2 is prime.
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%I #15 Sep 08 2022 08:46:07

%S 2,3,5,13,41,43,139,173,227,239,359,463,541,691,743,761,821,823,827,

%T 887,1021,1117,1289,1427,1489,1637,1723,1933,1999,2081,2287,2309,2719,

%U 2791,2833,2843,2953,3329,3541,3803,3823,3929,4003,4007,4079,4139,4297,4451,4561,4597,4691,4703,4817,4931,4943

%N Primes p such that prime(p) + 2*p^2 is prime.

%C The associated primes are: 11, 23, 41, 379, 3541, ...

%e 2 is in this sequence because 2 and prime(2) + 2*2^2 = 3 + 8 = 11 are both prime.

%t Select[Prime[Range[700]],PrimeQ[Prime[#]+2#^2]&] (* _Harvey P. Dale_, Mar 19 2018 *)

%o (Magma) [n: n in {1..5000} | IsPrime(n) and IsPrime(s) where s is (2*n^2 + NthPrime(n))];

%o (PARI) isok(p) = isprime(p) && isprime(prime(p) + 2*p^2); \\ _Michel Marcus_, Apr 13 2014

%Y Cf. A006450, A079704.

%K nonn

%O 1,1

%A _Ilya Lopatin_ and _Juri-Stepan Gerasimov_, Apr 13 2014