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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). 30

%I

%S 17,1277,113147,252277007,408936947,521481197,1116452627,1209950867,

%T 1645175087,2966003057,3947480417,6234613727,9307040837,9853497737,

%U 11878692167,13766391467,21956291867,22741837817,24388061207

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

%C Subsequence of A022012. - _R. J. Mathar_, Feb 10 2013

%C All terms congruent to 17 (modulo 30). - _Matt C. Anderson_, May 27 2015

%H 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 T. Forbes, <a href="http://anthony.d.forbes.googlepages.com/adf.htm">Prime k-tuplets</a>

%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;

%p end if ;

%p end proc:

%p p := [0, 2, 6, 12, 14, 20, 24, 26, 30]:

%p # using isprime(m*n+o+p)

%p o := 17:

%p m:=30:

%p loopstop:=10^11:

%p loopstart:=0:

%p for n from loopstart to loopstop do

%p counter := 0:

%p wc := 0;

%p wd := 0;

%p while `and`(wd > -10, wd < 9) do

%p wd := wd+1;

%p if composite_small(m*n+o+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;

%p if isprime(m*n+o+p[wc]) then counter := counter+1 else counter := -1 end if;

%p end do end if;

%p if counter = 9 then print(m*n+o) end if;

%p end do:

%t Select[Prime[Range[260000000]], Union[PrimeQ[ # +{2, 6, 12, 14, 20, 24, 26, 30}]]=={True} &] (* _Vincenzo Librandi_, May 27 2015 *)

%o (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 (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 (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

%K nonn

%O 1,1

%A _Warut Roonguthai_

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Last modified June 21 01:04 EDT 2021. Contains 345330 sequences. (Running on oeis4.)