A164570 Primes p such that 8*p-3 and 8*p+3 are also prime numbers.

2, 5, 7, 13, 47, 103, 107, 127, 163, 233, 293, 337, 383, 433, 443, 467, 503, 673, 677, 733, 797, 877, 1087, 1093, 1153, 1217, 1223, 1307, 1637, 1933, 2053, 2087, 2137, 2423, 2477, 2543, 2633, 2687, 2857, 2917, 3163, 3373, 3407, 3467, 3767, 3793, 3877

Offset

1,1

Comments

Subsequence of A023229. [R. J. Mathar, Aug 26 2009]

Primes of the form A087695(k)/8. [R. J. Mathar, Aug 26 2009]

Links

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

Example

For p=2, 8*2-3=13 and 8*2+3=19 are prime numbers, which adds p=2 to the sequence
For p=5, 8*5-3=37 and 8*5+3=43 are prime numbers, which adds p=5 to the sequence.

Mathematica

lst={}; Do[p=Prime[n]; If[PrimeQ[8*p-3]&&PrimeQ[8*p+3], AppendTo[lst, p]], {n, 7!}]; lst
Select[Prime[Range[1000]], And@@PrimeQ/@{8 # + 3, 8 # - 3}&] (* Vincenzo Librandi, Apr 09 2013 *)
Select[Prime[Range[1000]], AllTrue[8#+{3, -3}, PrimeQ]&] (* Harvey P. Dale, May 05 2023 *)

Prog

(Magma) [p: p in PrimesUpTo(3000) | IsPrime(8*p-3) and IsPrime(8*p+3)]; // Vincenzo Librandi, Apr 09 2013

Crossrefs

Cf. A023212, A023217, A023224, A023230, A023239, A060212, A106015, A124098, A125272, A127430, A153768, A164566, A164567, A164568, A164569.

Sequence in context: A141112 A053647 A023242 * A348671 A265811 A265793

Adjacent sequences: A164567 A164568 A164569 * A164571 A164572 A164573

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2009

Extensions

Comments turned into examples by R. J. Mathar, Aug 26 2009

Status

approved