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

%I A022006 #86 Nov 08 2023 11:27:03
%S A022006 5,11,101,1481,16061,19421,21011,22271,43781,55331,144161,165701,
%T A022006 166841,195731,201821,225341,247601,268811,326141,347981,361211,
%U A022006 397751,465161,518801,536441,633461,633791,661091,768191,795791,829721,857951,876011,958541
%N A022006 Initial members p of prime 5-tuples (p, p+2, p+6, p+8, p+12).
%C A022006 Subsequence of A007530. - _R. J. Mathar_, Feb 10 2013
%C A022006 All terms, except for the first one, are congruent to 11 (modulo 30). - _Matt C. Anderson_, May 22 2015
%C A022006 For n > 1 and p = a(n),  (p, p+2, p+6, p+8, p+12) are consecutive primes. - _Zak Seidov_, Jun 07 2017
%C A022006 A022007 is a similar sequence. - _Wolfdieter Lang_, Oct 06 2017
%H A022006 Dana Jacobsen, <a href="/A022006/b022006.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe, terms 1001..10000 from Matt C. Anderson)
%H A022006 J. K. Andersen, <a href="http://primerecords.dk/">Prime Records</a>.
%H A022006 Tony Forbes and Norman Luhn, <a href="http://www.pzktupel.de/ktuplets">Prime k-tuplets</a>.
%H A022006 Norman Luhn, <a href="http://www.pzktupel.de/smarchive.html">Table of n, a(n) for n = 1..1000000</a>.
%e A022006 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
%t A022006 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 *)
%t A022006 Transpose[Select[Partition[Prime[Range[64000]],5,1],Differences[#] == {2,4,2,4}&]][[1]] (* _Harvey P. Dale_, Dec 08 2014 *)
%o A022006 (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
%o A022006 (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
%o A022006 (Perl) use ntheory ":all"; say for sieve_prime_cluster(1,1e7, 2,6,8,12); # _Dana Jacobsen_, Sep 30 2015
%o A022006 (Python)
%o A022006 from sympy import primerange
%o A022006 def aupto(limit):
%o A022006   p, q, r, s, alst = 2, 3, 5, 7, []
%o A022006   for t in primerange(11, limit+13):
%o A022006     if p+2 == q and p+6 == r and p+8 == s and p+12 == t: alst.append(p)
%o A022006     p, q, r, s = q, r, s, t
%o A022006   return alst
%o A022006 print(aupto(10**6)) # _Michael S. Branicky_, May 11 2021
%Y A022006 Cf. A000040, A022007.
%K A022006 nonn
%O A022006 1,1
%A A022006 _Warut Roonguthai_
%E A022006 Missing terms a(51) and a(52) added in b-file by _Dana Jacobsen_, Sep 30 2015