A240838 Primes p such that prime(p) + 2*p^2 is prime.

2, 3, 5, 13, 41, 43, 139, 173, 227, 239, 359, 463, 541, 691, 743, 761, 821, 823, 827, 887, 1021, 1117, 1289, 1427, 1489, 1637, 1723, 1933, 1999, 2081, 2287, 2309, 2719, 2791, 2833, 2843, 2953, 3329, 3541, 3803, 3823, 3929, 4003, 4007, 4079, 4139, 4297, 4451, 4561, 4597, 4691, 4703, 4817, 4931, 4943

Offset: 1

Author

Ilya Lopatin and Juri-Stepan Gerasimov, Apr 13 2014

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

Cf. A006450, A079704.

Programs

Magma

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

Mathematica

Select[Prime[Range[700]],PrimeQ[Prime[#]+2#^2]&] (* Harvey P. Dale, Mar 19 2018 *)

PARI

isok(p) = isprime(p) && isprime(prime(p) + 2*p^2); \\ Michel Marcus, Apr 13 2014