1,1

In the first 10000 primes there are 5698 terms (~57% of the primes). In the 10000 primes from prime(1,000,000,000) to prime(1,000,010,000) there are 8432 primes in this sequence or ~84%. It seems likely the density of these terms within the primes slowly approaches 100%. This indicates the density of "Prime Septets", as defined in A268593 (which rely upon primes in the complement of this sequence), declines steadily at larger n. - Richard R. Forberg, Feb 12 2016

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

npQ[n_]:=Module[{c=2n}, !PrimeQ[c+3]&&!PrimeQ[c-3]]; Select[Prime[ Range[ 200]], npQ] (* Harvey P. Dale, Jan 21 2013 *)

Select[Prime[Range[200]], NoneTrue[2#+{3, -3}, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 25 2019 *)

(Magma) [p: p in PrimesUpTo(1100)| not IsPrime(2*p+3)and not IsPrime(2*p-3)]; // Vincenzo Librandi, Dec 08 2010

(PARI) isok(p) = isprime(p) && !isprime(2*p+3) && !isprime(2*p-3); \\ Michel Marcus, Feb 12 2016

Cf. A000040, A131426, A141468.

Sequence in context: A172462 A042739 A348570 * A172056 A032648 A235808

Adjacent sequences: A172253 A172254 A172255 * A172257 A172258 A172259

Juri-Stepan Gerasimov, Jan 30 2010

Corrected and extended by Vincenzo Librandi, Apr 01 2010

approved