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A027569 Initial members of prime decaplets (p, p+2, p+6, p+8, p+12, p+18, p+20, p+26, p+30, p+32).

%I A027569 #36 Nov 04 2021 13:06:37
%S A027569 11,33081664151,83122625471,294920291201,573459229151,663903555851,
%T A027569 688697679401,730121110331,1044815397161,1089869189021,1108671297731,
%U A027569 1235039237891,1291458592421,1738278660731
%N A027569 Initial members of prime decaplets (p, p+2, p+6, p+8, p+12, p+18, p+20, p+26, p+30, p+32).
%C A027569 All terms are congruent to 11 (modulo 210). - _Matt C. Anderson_, May 28 2015
%H A027569 Matt C. Anderson and Dana Jacobsen, <a href="/A027569/b027569.txt">Table of n, a(n) for n = 1..10000</a> [first 100 terms from Matt C. Anderson]
%H A027569 Tony Forbes and Norman Luhn, <a href="http://www.pzktupel.de/ktuplets.htm">Prime k-tuplets</a>
%H A027569 Norman Luhn, <a href="http://www.pzktupel.de/SMArchiv/10tup1.zip">1 million terms of A027569</a>, zip compressed (7.93 MB) (2021)
%p A027569 composite_small := proc (n::integer)
%p A027569 description "procedure to determine if n has a prime factor less than 100";
%p A027569 if igcd(2305567963945518424753102147331756070, n) = 1 then
%p A027569 return false else return true end if;
%p A027569 end proc;
%p A027569 # begin initialization section
%p A027569 p := [0, 2, 6, 8, 12, 18, 20, 26, 30, 32]; o := [1271, 1691]; m := 2310;
%p A027569 # end initialization section
%p A027569 with(ArrayTools); os := Size(o, 2); ps := Size(p, 2);
%p A027569 loopstop := 10^11; loopstart := 0;
%p A027569 print(11);
%p A027569 for n from loopstart to loopstop do
%p A027569 for a to os do
%p A027569 counter := 0; wc := 0; wd := 0;
%p A027569 while `and`(wd > -10, wd < ps) do
%p A027569 wd := wd+1;
%p A027569 if composite_small(m*n+o[a]+p[wd]) = false then wd := wd+1 else wd := -10 end if;
%p A027569 end do;
%p A027569 if wd >= 9 then while `and`(counter >= 0, wc < ps) do
%p A027569 wc := wc+1;
%p A027569 if isprime(m*n+o[a]+p[wc]) then counter := counter+1 else counter := -1 end if end do;
%p A027569 end if;
%p A027569 if counter = ps then print(m*n+o[a]); end if;
%p A027569 end do;
%p A027569 end do;
%p A027569 # _Matt C. Anderson_, Apr 30 2015
%o A027569 (PARI) is(n)=isprime(n) && isprime(n+2) && isprime(n+6) && isprime(n+8) && isprime(n+12) && isprime(n+18) && isprime(n+20) && isprime(n+26) && isprime(n+30) && isprime(n+32)
%o A027569 v=primes(10); t=1; forprime(p=31,1e11, v[t]=p; t=(t%10)+1; if(p-v[t]==32 && is(v[t]), print1(v[t]", "))) \\ _Charles R Greathouse IV_, May 20 2015
%o A027569 (Perl) use ntheory ":all"; say for sieve_prime_cluster(1,1e13, 2,6,8,12,18,20,26,30,32); # _Dana Jacobsen_, Sep 30 2015
%Y A027569 Cf. A027570, A202281, A202282.
%K A027569 nonn
%O A027569 1,1
%A A027569 _Warut Roonguthai_