A137703 Prime numbers p such that p +- ((p-1)/3) are primes.

991, 2143, 3331, 4591, 4663, 5563, 5653, 8623, 9181, 9343, 9631, 12781, 13033, 13411, 14851, 15643, 16183, 16363, 20161, 20521, 20593, 23311, 24373, 25471, 26641, 27073, 28711, 30133, 30763, 32401, 32491, 34381, 35803, 37783, 38431, 38611, 39043, 39241

Offset

1,1

Links

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

Example

991 is in the sequence because 991+(990/3) = 1321 and 991-(990/3) = 661, which are primes;
2143 is in the sequence because 2143+(2142/3) = 2857 and 2143-(2142/3) = 1429, which are primes.

Mathematica

Select[Prime[Range[50000]], PrimeQ[# + (# - 1) / 3]&&PrimeQ[# - (# - 1) / 3]&] (* Vincenzo Librandi, Jun 15 2013 *)

Prog

(Magma) [p: p in PrimesInInterval(5, 40000)| IsPrime((4*p-1) div 3 ) and IsPrime((2*p+1) div 3)]; // Vincenzo Librandi, Jun 15 2013

Crossrefs

Sequence in context: A053393 A365598 A031790 * A255098 A155509 A093177

Adjacent sequences: A137700 A137701 A137702 * A137704 A137705 A137706

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Apr 27 2008

Extensions

More terms from Vincenzo Librandi, Jun 15 2013

Status

approved