The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. Tony Forbes and Norman Luhn, Patterns of prime k-tuplets & the Hardy-Littlewood constants. 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 Adjacent sequences: A022006 A022007 A022008 * A022010 A022011 A022012 KEYWORD nonn AUTHOR Warut Roonguthai STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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