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A022009 Initial members of prime septuplets (p, p+2, p+6, p+8, p+12, p+18, p+20). 39
11, 165701, 1068701, 11900501, 15760091, 18504371, 21036131, 25658441, 39431921, 45002591, 67816361, 86818211, 93625991, 124716071, 136261241, 140117051, 154635191, 162189101, 182403491, 186484211, 187029371, 190514321, 198453371 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are congruent to 11 (modulo 210). - Matt C. Anderson, May 26 2015
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
See A343637 for the least prime septuplets > 10^n, n >= 0. - M. F. Hasler, Aug 04 2021
LINKS
Dana Jacobsen, Table of n, a(n) for n = 1..10000 (first 1000 terms from Matt C. Anderson)
Matt C. Anderson, table of prime k-tuplets.
Norman Luhn, 1 million terms, zipped archive.
Vladimir Shevelev and Peter J. C. Moses, Constellations of primes generated by twin primes, arXiv:1610.03385 [math.NT], 2016.
Eric Weisstein's World of Mathematics, Prime Constellation.
FORMULA
a(n) = 210*A182387(n) + 11. - Hugo Pfoertner, Nov 18 2022
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Cf. A022010 (septuplets of the second type), A182387, A276826, A276848, A343637 (septuplet following 10^n).
Sequence in context: A055311 A116622 A013794 * A201249 A144837 A324267
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified June 17 15:26 EDT 2024. Contains 373456 sequences. (Running on oeis4.)