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%I #66 Nov 04 2023 13:52:44
%S 11,165701,1068701,11900501,15760091,18504371,21036131,25658441,
%T 39431921,45002591,67816361,86818211,93625991,124716071,136261241,
%U 140117051,154635191,162189101,182403491,186484211,187029371,190514321,198453371
%N Initial members of prime septuplets (p, p+2, p+6, p+8, p+12, p+18, p+20).
%C All terms are congruent to 11 (modulo 210). - _Matt C. Anderson_, May 26 2015
%C Also the terms k of A276848 for which k == 1 (mod 10), see the comment in A276848 and A276826. All terms are obviously also congruent to 11 (modulo 30). - _Vladimir Shevelev_, Sep 21 2016
%C See A343637 for the least prime septuplets > 10^n, n >= 0. - _M. F. Hasler_, Aug 04 2021
%H Dana Jacobsen, <a href="/A022009/b022009.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Matt C. Anderson)
%H Matt C. Anderson, <a href="https://sites.google.com/site/primeconstellations/">table of prime k-tuplets</a>.
%H Tony Forbes and Norman Luhn, <a href="https://pzktupel.de/ktpatt_hl.php">Patterns of prime k-tuplets & the Hardy-Littlewood constants</a>.
%H Norman Luhn, <a href="https://pzktupel.de/SMArchiv/07tup1.zip">1 million terms</a>, zipped archive.
%H Vladimir Shevelev and Peter J. C. Moses, <a href="https://arxiv.org/abs/1610.03385">Constellations of primes generated by twin primes</a>, arXiv:1610.03385 [math.NT], 2016.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeConstellation.html">Prime Constellation</a>.
%F a(n) = 210*A182387(n) + 11. - _Hugo Pfoertner_, Nov 18 2022
%t Transpose[Select[Partition[Prime[Range[10400000]],7,1],Differences[#] == {2,4,2,4,6,2}&]][[1]] (* _Harvey P. Dale_, Jul 13 2014 *)
%t Select[Prime[Range[2 10^8]], Union[PrimeQ[# + {2, 6, 8, 12, 18, 20}]] == {True} &] (* _Vincenzo Librandi_, Oct 01 2015 *)
%o (PARI) nextcomposite(n)=if(n<4, return(4)); n=ceil(n); if(isprime(n), n+1, n)
%o is(n)=if(n%30!=11 || !isprime(n) || !isprime(n+2), return(0)); my(p=n, q=n+2, k=2, f); while(p!=q && q-p<7, f=if(isprime(k++), nextprime, nextcomposite); p=f(p+1); q=f(q+1)); p==q \\ _Charles R Greathouse IV_, Sep 30 2016
%o (PARI) select( {is_A022009(n)=n%210==11&&!foreach([20,18,12,8,6,2,0],d,isprime(n+d)||return)}, [11+k*210|k<-[0..10^5]]) \\ _M. F. Hasler_, Aug 04 2021
%o (Perl) use ntheory ":all"; say for sieve_prime_cluster(1,1e9, 2,6,8,12,18,20); # _Dana Jacobsen_, Sep 30 2015
%o (Magma) [p: p in PrimesUpTo(2*10^8) | forall{p+r: r in [2,6,8,12,18,20] | IsPrime(p+r)}]; // _Vincenzo Librandi_, Oct 01 2015
%Y Cf. A022010 (septuplets of the second type), A182387, A276826, A276848, A343637 (septuplet following 10^n).
%K nonn
%O 1,1
%A _Warut Roonguthai_
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