

A046119


Middle member of a sexy prime triple: value of p+6 such that p, p+6 and p+12 are all prime, but p+18 is not (although p6 might be).


4



13, 23, 37, 53, 73, 103, 107, 157, 173, 233, 263, 277, 353, 373, 563, 593, 613, 653, 733, 947, 977, 1103, 1123, 1187, 1223, 1283, 1297, 1367, 1433, 1453, 1493, 1613, 1663, 1753, 1783, 1873, 1907, 1993, 2137, 2287, 2383, 2417, 2683, 2693, 2713
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OFFSET

1,1


COMMENTS

p6 will be prime if the prime triple contains the last 3 primes of a sexy prime quadruple.
If a sexy prime triple happens to include the last 3 members of a sexy prime quadruple, this sequence will contain the sexy prime triple's middle member; e.g., a(4)=53 is the middle member of the sexy prime triple (47, 53, 59), but is also the third member of the sexy prime quadruple (41, 47, 53, 59).  Daniel Forgues, Aug 05 2009


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Sexy Primes.


FORMULA

a(n) = A046118(n) + 6.  Michel Marcus, Jan 06 2015


MATHEMATICA

lst={}; Do[p=Prime[n]; If[PrimeQ[p+6]&&PrimeQ[p+12]&&!PrimeQ[p+18], AppendTo[lst, p+6]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 29 2008 *)
Select[Prime[Range[400]], And@@PrimeQ[{#6, #+6}]&&!PrimeQ[#+12]&] (* Harvey P. Dale, Nov 01 2011 *)


CROSSREFS

Cf. A023201, A046117.
Cf. A046118, A046120.
Sequence in context: A050857 A089714 A070219 * A164408 A164416 A164491
Adjacent sequences: A046116 A046117 A046118 * A046120 A046121 A046122


KEYWORD

nonn


AUTHOR

Eric W. Weisstein


EXTENSIONS

Definition edited by Daniel Forgues, Aug 12 2009


STATUS

approved



