A247197 Primes p such that 2*p^2 + 3 and 2*p^2 + 5 are also primes.

2, 7, 23, 47, 887, 1297, 1657, 2207, 2357, 2753, 4583, 4657, 6967, 8353, 8363, 10453, 12203, 12343, 13967, 16217, 16903, 21737, 23357, 23497, 25447, 29017, 32363, 36083, 40847, 41603, 41617, 43633, 45757, 46933, 48407, 52313, 60167, 60457, 66173, 67867, 71713, 72497, 72823, 73897

Offset

1,1

Comments

Primes in A247175.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

2 is in this sequence because 2*2^2 + 3 = 11, 2*2^2 + 5 = 13 and 2 are all primes.

Mathematica

a247197[n_Integer] := Select[Prime /@ Range[n], And[PrimeQ[2*#^2 + 3], PrimeQ[2*#^2 + 5]] &]; a247197[7500] (* Michael De Vlieger, Nov 30 2014 *)
Select[Prime[Range[7300]], AllTrue[2#^2+{3, 5}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 21 2019 *)

Prog

(Magma) [ n: n in [1..70000] | IsPrime(n) and IsPrime(2*(n^2+2)-1) and IsPrime(2*(n^2+2)+1) ];

Crossrefs

Cf. A247101, A247175, A249446.

Sequence in context: A247175 A049001 A049002 * A195629 A323526 A011757

Adjacent sequences: A247194 A247195 A247196 * A247198 A247199 A247200

Keyword

nonn

Author

Juri-Stepan Gerasimov, Nov 30 2014

Status

approved