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A022548 Initial members of prime nonuplets (p, p+4, p+10, p+12, p+18, p+22, p+24, p+28, p+30).

%I A022548 #33 Oct 24 2021 08:41:44
%S A022548 88789,855709,74266249,964669609,1422475909,2117861719,2558211559,
%T A022548 2873599429,5766036949,6568530949,8076004609,9853497739,16394542249,
%U A022548 21171795079,21956291869,22741837819,26486447149,27254489389
%N A022548 Initial members of prime nonuplets (p, p+4, p+10, p+12, p+18, p+22, p+24, p+28, p+30).
%C A022548 All terms are congruent to 169 (modulo 210). - _Matt C. Anderson_, May 28 2015
%H A022548 Matt C. Anderson and Dana Jacobsen, <a href="/A022548/b022548.txt">Table of n, a(n) for n = 1..10000</a> [first 800 terms from Matt C. Anderson]
%H A022548 Tony Forbes and Norman Luhn, <a href="http://www.pzktupel.de/ktuplets">Prime k-tuplets</a>
%H A022548 Norman Luhn, <a href="http://www.pzktupel.de/SMArchiv/09tup4.zip">The first 10^6 initial members of prime 9-tuplets | pattern: d= 0, 4, 10, 12, 18, 22, 24, 28, 30</a>, zip archive.
%p A022548 a := 1; for b to 25 do a := a*ithprime(b) end do; a;
%p A022548 # so ‘a’ is the product of the primes 2 through 97
%p A022548 composite_small := proc (n::integer)
%p A022548 description "determine if n has a prime factor less than 100";
%p A022548 if igcd(2305567963945518424753102147331756070, n) = 1 then return false else return true end if
%p A022548 end proc;
%p A022548 # my technique involves isprime(m*n+o+p)
%p A022548 # with Multiplier, Number, Offset, and Pattern
%p A022548 p := [0, 4, 10, 12, 18, 22, 24, 28, 30];
%p A022548 o := [2059, 6679, 7519, 8989, 10249, 12139, 14449, 14869, 15919, 17179, 20539, 21379, 24109, 25999, 28729];
%p A022548 with(ArrayTools);
%p A022548 os := Size(o, 2);
%p A022548 ps := Size(p, 2);
%p A022548 m := 30030;
%p A022548 loopstop := 10^11;
%p A022548 loopstart := 0;
%p A022548 for n from loopstart to loopstop do
%p A022548 for a to os do
%p A022548 counter := 0; wc := 0; wd := 0;
%p A022548 while `and`(wd > -10, wd < ps) do
%p A022548 wd := wd+1;
%p A022548 if composite_small(m*n+o[a]+p[wd]) = false then wd := wd+1 else wd := -10 end if;
%p A022548 end do;
%p A022548 if wd >= 9 then
%p A022548 while `and`(counter >= 0, wc < ps) do
%p A022548 wc := wc+1;
%p A022548 if isprime(m*n+o[a]+p[wc]) then counter := counter+1 else counter := -1 end if;
%p A022548 end do;
%p A022548 end if;
%p A022548 if counter = ps then print(m*n+o[a]) end if;
%p A022548 end do;
%p A022548 end do;
%p A022548 # _Matt C. Anderson_, Feb 13 2014
%t A022548 Select[Prime[Range[2 10^6]], Union[PrimeQ[# + {4, 10, 12, 18, 22, 24, 28, 30}]] == {True} &] (* _Vincenzo Librandi_, Sep 30 2015 *)
%o A022548 (Perl) use ntheory ":all"; say for sieve_prime_cluster(1,1e11, 4,10,12,18,22,24,28,30); # _Dana Jacobsen_, Sep 30 2015
%o A022548 (PARI) forprime(p=2, 10^30, if (isprime(p+4) && isprime(p+10) && isprime(p+12) && isprime(p+18) && isprime(p+22) && isprime(p+24) && isprime(p+28) && isprime(p+30), print1(p", "))) \\ _Altug Alkan_, Sep 30 2015
%Y A022548 Cf. A022545, A022546, A022547.
%K A022548 nonn
%O A022548 1,1
%A A022548 _Warut Roonguthai_