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A022009 Initial members of prime septuplets (p, p+2, p+6, p+8, p+12, p+18, p+20). 35

%I

%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 n of A276848 for which n == 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

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

%H Vladimir Shevelev, 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 W. Weisstein, <a href="http://mathworld.wolfram.com/PrimeConstellation.html">Prime Constellation</a> (MathWorld)

%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 (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

%K nonn

%O 1,1

%A _Warut Roonguthai_

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Last modified February 27 15:59 EST 2020. Contains 332307 sequences. (Running on oeis4.)