A143794 Primes p, with index k, such that p-k and p+k are both prime.

7, 13, 61, 181, 317, 827, 1831, 2657, 2801, 3181, 3739, 4093, 4561, 5011, 5443, 5531, 5653, 6359, 6659, 9029, 10729, 11383, 13109, 13907, 14489, 15217, 15859, 16603, 17581, 20393, 21499, 23537, 25037, 25169, 26153, 26959, 27077, 27803, 27851

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Sep 01 2008

Keywords

• nonn

Examples

			7 = prime(4) and both 7 - 4 = 3 and 7 + 4 = 11 are prime;
13 = prime(6) and both 13 - 6 = 7 and 13 + 6 = 19 are prime;
61 = prime(18) and both 61 - 18 = 43 and 61 + 18 = 79 are prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A064403 (corresponding prime indices).

Programs

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[p-n]&&PrimeQ[p+n],AppendTo[lst,p]],{n,8!}];lst
Transpose[Select[Table[{n,Prime[n]},{n,3100}],And@@PrimeQ[{Last[#]- First[#],Total[#]}]&]][[2]] (* Harvey P. Dale, Nov 04 2011 *)

PARI

n=0;forprime(p=2,1e5,if(isprime(p-n++)&&isprime(p+n),print1(p", "))) \\ Charles R Greathouse IV, Nov 04 2011

Extensions

Definition edited by Harvey P. Dale, Nov 04 2011