A162001 Initial members of prime triples (p, p+2, p+6) for which also the sum 3p+8 is prime.

5, 11, 17, 41, 101, 311, 347, 641, 857, 1301, 1427, 1481, 2237, 2687, 3461, 3527, 4001, 4787, 8861, 10457, 11171, 11777, 13691, 14627, 19421, 19991, 21017, 21557, 22271, 24917, 25997, 26261, 26681, 26711, 27737, 29021, 31511, 32057, 33347, 35591

Offset: 1

Author

Milton L. Brown (miltbrown(AT)earthlink.net), Jun 24 2009

Keywords

• nonn

Comments

A subsequence of A022004 (= initial members of prime triples (p, p+2, p+6)). - Emeric Deutsch, Jul 12 2009

Examples

			(5,7,11) => 23 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A162001.

Cf. A022004, A376013.

Programs

Maple

a := proc (n) if isprime(n) = true and isprime(n+2) = true and isprime(n+6) = true and isprime(3*n+8) = true then n else end if end proc: seq(a(n), n = 1 .. 50000); # Emeric Deutsch, Jul 12 2009

Mathematica

Select[Select[Partition[Prime[Range[4000]], 3, 1], Differences[#] == {2, 4} &], PrimeQ[Total[#]] &][[;; , 1]] (* Amiram Eldar, Sep 06 2024 *)

PARI

list(lim)=my(v=List(), p=5, q=7, s); forprime(r=11, lim+6, if(r-p==6 && q-p==2 && isprime(s=3*p+8), listput(v, p)); p=q; q=r); Vec(v) \\ Charles R Greathouse IV, Sep 19 2024

Formula

a(n) == 5 (mod 6). - Hugo Pfoertner, Sep 06 2024

a(n) = (A376013(n) - 8)/3. - Amiram Eldar, Sep 06 2024

a(n) >> n log^4 n. - Charles R Greathouse IV, Sep 19 2024

Extensions

Definition corrected by Emeric Deutsch, Jul 12 2009

Extended by Emeric Deutsch, Jul 12 2009