A022009 Initial members of prime septuplets (p, p+2, p+6, p+8, p+12, p+18, p+20).
11, 165701, 1068701, 11900501, 15760091, 18504371, 21036131, 25658441, 39431921, 45002591, 67816361, 86818211, 93625991, 124716071, 136261241, 140117051, 154635191, 162189101, 182403491, 186484211, 187029371, 190514321, 198453371
Offset: 1
Keywords
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.
Crossrefs
Programs
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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 -
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 *) -
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
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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
Formula
a(n) = 210*A182387(n) + 11. - Hugo Pfoertner, Nov 18 2022
Comments