A092058 Numbers n such that 2*prime(n)^2 - 1 is prime.

1, 2, 4, 5, 6, 7, 13, 14, 17, 21, 29, 30, 31, 33, 37, 41, 42, 45, 46, 47, 54, 56, 59, 62, 64, 71, 73, 75, 80, 81, 84, 93, 103, 105, 106, 113, 114, 120, 126, 131, 132, 134, 139, 141, 144, 145, 146, 148, 159, 160, 169, 175, 179, 183, 185, 186, 188, 192, 212, 217, 220

Offset: 1

Author

mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Feb 19 2004

Keywords

• easy
• nonn

Examples

			2*prime(1)^2 - 1 = 7 is prime so a(1)=1;
2*prime(2)^2 - 1 = 17 is prime so a(2)=2;
2*prime(3)^2 - 1 = 97 is not prime;
2*prime(4)^2 - 1 = 241 is prime so a(3)=4.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A092057.

Programs

Magma

[n: n in [1..220]| IsPrime(2*NthPrime(n)^2-1)]; // Vincenzo Librandi, Jan 18 2013

Mathematica

Select[Range[500],PrimeQ[2Prime[#]^2-1]&] (* Harvey P. Dale, Dec 13 2010 *)

PARI

for (i=1,300,if(isprime(2*prime(i)^2-1),print1(i,",")))

Formula

A106483(n) = prime(a(n)) . - R. J. Mathar, Aug 20 2019