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A022009
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Initial members of prime septuplets (p, p+2, p+6, p+8, p+12, p+18, p+20).
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39
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11, 165701, 1068701, 11900501, 15760091, 18504371, 21036131, 25658441, 39431921, 45002591, 67816361, 86818211, 93625991, 124716071, 136261241, 140117051, 154635191, 162189101, 182403491, 186484211, 187029371, 190514321, 198453371
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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MATHEMATICA
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Transpose[Select[Partition[Prime[Range[10400000]], 7, 1], Differences[#] == {2, 4, 2, 4, 6, 2}&]][[1]] (* Harvey P. Dale, Jul 13 2014 *)
Select[Prime[Range[2 10^8]], Union[PrimeQ[# + {2, 6, 8, 12, 18, 20}]] == {True} &] (* Vincenzo Librandi, Oct 01 2015 *)
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PROG
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(PARI) nextcomposite(n)=if(n<4, return(4)); n=ceil(n); if(isprime(n), n+1, n)
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
(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
(Perl) use ntheory ":all"; say for sieve_prime_cluster(1, 1e9, 2, 6, 8, 12, 18, 20); # Dana Jacobsen, Sep 30 2015
(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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