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A022546 Initial members of prime nonuplets (p, p+2, p+6, p+12, p+14, p+20, p+24, p+26, p+30).

%I A022546 #42 Sep 08 2022 08:44:46
%S A022546 17,1277,113147,252277007,408936947,521481197,1116452627,1209950867,
%T A022546 1645175087,2966003057,3947480417,6234613727,9307040837,9853497737,
%U A022546 11878692167,13766391467,21956291867,22741837817,24388061207
%N A022546 Initial members of prime nonuplets (p, p+2, p+6, p+12, p+14, p+20, p+24, p+26, p+30).
%C A022546 Subsequence of A022012. - _R. J. Mathar_, Feb 10 2013
%C A022546 All terms congruent to 17 (modulo 30). - _Matt C. Anderson_, May 27 2015
%H A022546 Matt C. Anderson and Dana Jacobsen, <a href="/A022546/b022546.txt">Table of n, a(n) for n = 1..10000</a> [first 200 terms from Matt C. Anderson]
%H A022546 Tony Forbes and Norman Luhn, <a href="http://www.pzktupel.de/ktuplets">Prime k-tuplets</a>
%H A022546 Norman Luhn, <a href="http://www.pzktupel.de/SMArchiv/09tup3.zip">The first 10^6 initial members of prime 9-tuplets | pattern: d= 0, 2, 6, 12, 14, 20, 24, 26, 30</a>, zip archive.
%p A022546 composite_small := proc (n::integer)
%p A022546 description "determine if n has a prime factor less than 100";
%p A022546 if igcd(2305567963945518424753102147331756070, n) = 1 then return false else return true;
%p A022546 end if ;
%p A022546 end proc:
%p A022546 p := [0, 2, 6, 12, 14, 20, 24, 26, 30]:
%p A022546 # using isprime(m*n+o+p)
%p A022546 o := 17:
%p A022546 m:=30:
%p A022546 loopstop:=10^11:
%p A022546 loopstart:=0:
%p A022546 for n from loopstart to loopstop do
%p A022546 counter := 0:
%p A022546 wc := 0;
%p A022546 wd := 0;
%p A022546 while `and`(wd > -10, wd < 9) do
%p A022546 wd := wd+1;
%p A022546 if composite_small(m*n+o+p[wd]) = false then wd := wd+1 else wd := -10 end if ;
%p A022546 end do;
%p A022546 if wd >= 9 then
%p A022546 while `and`(counter >= 0, wc < 9) do
%p A022546 wc := wc+1;
%p A022546 if isprime(m*n+o+p[wc]) then counter := counter+1 else counter := -1 end if;
%p A022546 end do end if;
%p A022546 if counter = 9 then print(m*n+o) end if;
%p A022546 end do:
%t A022546 Select[Prime[Range[260000000]], Union[PrimeQ[ # +{2, 6, 12, 14, 20, 24, 26, 30}]]=={True} &] (* _Vincenzo Librandi_, May 27 2015 *)
%o A022546 (Magma) [p: p in PrimesUpTo(260000000) | forall{p+r: r in [2, 6, 12,14,20,24,26,30] | IsPrime(p+r)}]; // _Vincenzo Librandi_, May 27 2015
%o A022546 (Perl) use ntheory ":all"; say for sieve_prime_cluster(1,1e11, 2,6,12,14,20,24,26,30); # _Dana Jacobsen_, Sep 30 2015
%o A022546 (PARI) forprime(p=2, 1e30, if (isprime(p+2) && isprime(p+6) && isprime(p+12) && isprime(p+14) && isprime(p+20) && isprime(p+24) && isprime(p+26) && isprime(p+30) , print1(p", "))) \\ _Altug Alkan_, Sep 30 2015
%Y A022546 Cf. A022545, A022547, A022548.
%K A022546 nonn
%O A022546 1,1
%A A022546 _Warut Roonguthai_