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A164570
Primes p such that 8*p-3 and 8*p+3 are also prime numbers.
1
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
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Comments turned into examples by R. J. Mathar, Aug 26 2009
STATUS
approved