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

1,1

Comments

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

Links

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

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

Example

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

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 *)

Prog

(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

Crossrefs

Subsequence of A162001.

Cf. A022004, A376013.

Sequence in context: A022004 A339503 A172454 * A171713 A375313 A174858

Adjacent sequences: A161998 A161999 A162000 * A162002 A162003 A162004

Keyword

nonn

Author

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

Extensions

Definition corrected by Emeric Deutsch, Jul 12 2009

Extended by Emeric Deutsch, Jul 12 2009

Status

approved