A275682 Table read by rows: list of sexy prime quadruples (p, p+6, p+12, p+18) such that p+24 is composite.

11, 17, 23, 29, 41, 47, 53, 59, 61, 67, 73, 79, 251, 257, 263, 269, 601, 607, 613, 619, 641, 647, 653, 659, 1091, 1097, 1103, 1109, 1481, 1487, 1493, 1499, 1601, 1607, 1613, 1619, 1741, 1747, 1753, 1759, 1861, 1867, 1873, 1879, 2371, 2377, 2383, 2389

Offset: 1

Author

Arkadiusz Wesolowski, Aug 05 2016

Keywords

• nonn
• tabf

Comments

(5, 11, 17, 23, 29) is a sexy prime 5-tuple and this is the only sexy prime 5-tuple.

Essentially same as A123083.

Examples

			The table starts:
11, 17, 23, 29;
41, 47, 53, 59;
61, 67, 73, 79;
...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2100
• Wikipedia, Sexy prime
• Index entries for primes, gaps between

Crossrefs

Cf. A023201, A023271, A123083, A275681.

Programs

Magma

lst:=[]; for p in PrimesInInterval(7, 2371) do b:=p+6; if IsPrime(b) then c:=b+6; if IsPrime(c) then d:=c+6; if IsPrime(d) then lst:=lst cat [p, b, c, d]; end if; end if; end if; end for; lst;

Mathematica

Most[#]&/@Select[Table[n + {0, 6, 12, 18, 24}, {n, Prime[Range[200]]}], PrimeQ[#]=={True, True, True, True, False}&]//Flatten (* Vincenzo Librandi, Jun 09 2017 *)
#+{0,6,12,18}&/@Select[Prime[Range[400]],AllTrue[#+{6,12,18},PrimeQ] && CompositeQ[#+24]&]//Flatten (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 29 2019 *)

Formula

a(n) = A123083(n+4).