

A022006


Initial members p of prime quintuplets (p, p+2, p+6, p+8, p+12).


68



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
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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
This sequence gives the initial prime members of the admissible 5tuple (0, 2, 6, 8, 12). This is shown by the sequence [1, 1, 4, 3, 3 ,repeat(1)], for n >= 1, whose members define the residue classes modulo prime(n) = A000040(n) which contain none of the 5tuple elements. It is one of two prime constellations of diameter 12. The other one has initial members given by A022007. See this for references.  Wolfdieter Lang, Oct 06 2017


LINKS

T. D. Noe and Matt C. Anderson and Dana Jacobsen, Table of n, a(n) for n = 1..10000 [first 10000 terms from Matt C. Anderson and first 1000 terms from T. D. Noe]
J. K. Andersen, Prime Records
T. Forbes, Prime ktuplets


EXAMPLE

Admissible 5tuple 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


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 bfile by Dana Jacobsen, Sep 30 2015


STATUS

approved



