A057326 First member of a prime triple in a 2p-1 progression.

2, 19, 79, 331, 439, 499, 619, 829, 1069, 1279, 1531, 2089, 2131, 2179, 2311, 2791, 3019, 3061, 3109, 3181, 3769, 4159, 4231, 4261, 4621, 4639, 4861, 4951, 5419, 5749, 6121, 6211, 6709, 6841, 7369, 7411, 7561, 7639, 8209, 8629, 9109, 9199, 9319, 9739, 10321, 10831

Offset: 1

Author

Patrick De Geest, Aug 15 2000

Keywords

• nonn

Comments

Numbers n such that n remains prime through 2 iterations of function f(x) = 2x - 1.

Examples

			Triplets are (2,3,5), (19,37,73), (79,157,313), (331,661,1321), ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2100
• Index entries for sequences related to primes in arithmetic progressions

Crossrefs

Cf. (A005382 and A005383), A057327, A057328, A057329, A057330, A005603.

Programs

Magma

[p: p in PrimesUpTo (10000) | IsPrime(2*p-1) and IsPrime(4*p-3)]; // K. D. Bajpai, Jun 26 2017

Maple

select(p -> andmap(isprime,[p, 2*p-1, 4*p-3]), [seq(p, p=0..10000)]); # K. D. Bajpai, Jun 26 2017

Mathematica

Select[Prime[Range[1500]],And@@PrimeQ[NestList[2#-1&,#,2]]&] (* Harvey P. Dale, Dec 09 2011 *)

PARI

forprime(p= 1, 100000, if(isprime(2*p-1) && isprime(4*p-3), print1(p, ", "))); \\ K. D. Bajpai, Jun 26 2017

Extensions

Offset set to 1 by Michel Marcus, Jul 02 2017