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%I #39 Sep 08 2022 08:44:46
%S 13,113143,626927443,2335215973,3447123283,4086982633,4422726013,
%T 6318867403,7093284043,8541306853,10998082213,14005112893,18869466373,
%U 21528117883,21843411823,28156779793,30303283243
%N Initial members of prime nonuplets (p, p+4, p+6, p+10, p+16, p+18, p+24, p+28, p+30).
%C All terms are congruent to 13 (modulo 30). - _Matt C. Anderson_, May 28 2015
%H Matt C. Anderson and Dana Jacobsen, <a href="/A022547/b022547.txt">Table of n, a(n) for n = 1..10000</a> [first 1000 terms from Matt C. Anderson]
%H Tony Forbes and Norman Luhn, <a href="http://www.pzktupel.de/ktuplets">Prime k-tuplets</a>
%H Norman Luhn, <a href="http://www.pzktupel.de/SMArchiv/09tup2.zip">The first 10^6 initial members of prime 9-tuplets | pattern: d= 0, 4, 6, 10, 16, 18, 24, 28, 30</a>, zip archive.
%p composite_small := proc (n::integer)
%p description "determine if n has a prime factor less than 100";
%p if igcd(2305567963945518424753102147331756070, n) = 1 then return false else return true end if;
%p end proc:
%p # A prime constellation pattern of length 9
%p p := [0, 4, 6, 10, 16, 18, 24, 28, 30];
%p # using isprime(m*n+o+p)
%p o := [1273, 2263, 2683, 4003, 4633, 4993, 5893, 6883, 6943, 8623, 9613, 10243, 11563, 12823, 14863, 15133, 15553, 17863, 18433, 19753, 21163, 21793, 22483, 23053, 23113, 24103, 25783, 27733, 28723, 29983]:
%p with(ArrayTools):
%p os := Size(o, 2):
%p m := 30030:
%p loopstop := 10^11:
%p loopstart := 0:
%p print(13);
%p for n from loopstart to loopstop do
%p for a from 1 to os do
%p counter := 0; wc := 0; wd := 0;
%p while `and`(wd > -10, wd < 9) do
%p wd := wd+1;
%p if composite_small(m*n+o[a]+p[wd]) = false then wd := wd+1 else wd := -10 end if
%p end do;
%p if wd >= 9 then
%p while `and`(counter >= 0, wc < 9) do
%p wc := wc+1; if isprime(m*n+o[a]+p[wc]) then counter := counter+1 else counter := -1 end if;
%p end do;
%p end if;
%p if counter = 9 then print(m*n+o[a]) end if;
%p end do:
%p end do:
%p # _Matt C. Anderson_, Feb 01 2014
%t Select[Prime[Range[200000]], Union[PrimeQ[# + {4, 6, 10, 16, 18, 24, 28, 30}]] == {True} &] (* _Vincenzo Librandi_, Sep 30 2015 *)
%o (Perl) use ntheory ":all"; say for sieve_prime_cluster(1,1e11, 4,6,10,16,18,24,28,30); # _Dana Jacobsen_, Sep 30 2015
%o (Magma) [p: p in PrimesUpTo(2*10^8) | forall{p+r: r in [4,6,10,16,18,24,28,30] | IsPrime(p+r)}]; // _Vincenzo Librandi_, Sep 30 2015
%o (PARI) forprime(p=2, 10^30, if (isprime(p+4) && isprime(p+6) && isprime(p+10) && isprime(p+16) && isprime(p+18) && isprime(p+24) && isprime(p+28) && isprime(p+30), print1(p", "))) \\ _Altug Alkan_, Sep 30 2015
%Y Cf. A022545, A022546, A022548.
%K nonn
%O 1,1
%A _Warut Roonguthai_
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