A022006 Initial members p of prime 5-tuples (p, p+2, p+6, p+8, p+12).

5, 11, 101, 1481, 16061, 19421, 21011, 22271, 43781, 55331, 144161, 165701, 166841, 195731, 201821, 225341, 247601, 268811, 326141, 347981, 361211, 397751, 465161, 518801, 536441, 633461, 633791, 661091, 768191, 795791, 829721, 857951, 876011, 958541

Offset

1,1

Comments

Subsequence of A007530. - R. J. Mathar, Feb 10 2013

All terms, except for the first one, are congruent to 11 (modulo 30). - Matt C. Anderson, May 22 2015

For n > 1 and p = a(n), (p, p+2, p+6, p+8, p+12) are consecutive primes. - Zak Seidov, Jun 07 2017

A022007 is a similar sequence. - Wolfdieter Lang, Oct 06 2017

Links

Dana Jacobsen, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe, terms 1001..10000 from Matt C. Anderson)

J. K. Andersen, Prime Records.

Tony Forbes and Norman Luhn, Prime k-tuplets.

Norman Luhn, Table of n, a(n) for n = 1..1000000.

Example

Admissible 5-tuple guaranteeing sequence example: for prime(3) = 5 the first residue class starting with a nonnegative number and containing none of the members of (0, 2, 6, 8, 12) is 4 (mod 5). - Wolfdieter Lang, Oct 06 2017

Mathematica

lst={}; Do[p=Prime[n]; If[PrimeQ[p+2]&&PrimeQ[p+6]&&PrimeQ[p+8]&&PrimeQ[p+12], AppendTo[lst, p]], {n, 9!}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 25 2008 *)
Transpose[Select[Partition[Prime[Range[64000]], 5, 1], Differences[#] == {2, 4, 2, 4}&]][[1]] (* Harvey P. Dale, Dec 08 2014 *)

Prog

(PARI) forprime(p=2, 1e7, if(isprime(p+2) && isprime(p+6) && isprime(p+8) && isprime(p+12), print1(p", "))) \\ Charles R Greathouse IV, Jul 19 2011
(Magma) [p: p in PrimesUpTo(2*10^6) | IsPrime(p+2) and IsPrime(p+6) and IsPrime(p+8) and IsPrime(p+12)]; // Vincenzo Librandi, May 23 2015
(Perl) use ntheory ":all"; say for sieve_prime_cluster(1, 1e7, 2, 6, 8, 12); # Dana Jacobsen, Sep 30 2015
(Python)
from sympy import primerange
def aupto(limit):
  p, q, r, s, alst = 2, 3, 5, 7, []
  for t in primerange(11, limit+13):
    if p+2 == q and p+6 == r and p+8 == s and p+12 == t: alst.append(p)
    p, q, r, s = q, r, s, t
  return alst
print(aupto(10**6)) # Michael S. Branicky, May 11 2021

Crossrefs

Cf. A000040, A022007.

Sequence in context: A157967 A088268 A030085 * A201074 A056111 A090160

Adjacent sequences: A022003 A022004 A022005 * A022007 A022008 A022009

Keyword

nonn

Author

Warut Roonguthai

Extensions

Missing terms a(51) and a(52) added in b-file by Dana Jacobsen, Sep 30 2015

Status

approved