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A023271
Primes p such that p, p+6, p+12, p+18 are all primes.
23
5, 11, 41, 61, 251, 601, 641, 1091, 1481, 1601, 1741, 1861, 2371, 2671, 3301, 3911, 4001, 5101, 5381, 5431, 5641, 6311, 6361, 9461, 11821, 12101, 12641, 13451, 14621, 14741, 15791, 15901, 17471, 18211, 19471, 20341, 21481, 23321, 24091, 26171, 26681
OFFSET
1,1
COMMENTS
Smallest member of a "sexy" prime quadruple.
For n > 1, a(n) ends in 1. - Robert Israel, Jul 16 2015
The only sexy prime quintuple corresponding to (p, p+6, p+12, p+18, p+24) starts with a(1) = 5, so this quintuple is (5, 11, 17, 23, 29) (see Wikipedia link and A206039). - Bernard Schott, Mar 10 2023
LINKS
Matt C. Anderson and Robert Israel, Table of n, a(n) for n = 1..10000 (n = 1..100 from Matt C. Anderson)
Eric Weisstein's World of Mathematics, Sexy Primes. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes. - N. J. A. Sloane, Mar 07 2021]
Wikipedia, Sexy prime.
MAPLE
for a to 2*10^5 do
if `and`(isprime(a), isprime(a+6), isprime(a+12), isprime(a+18))
then print(a);
end if;
end do;
# code produces 109 primes
# Matt C. Anderson, Jul 15 2015
MATHEMATICA
Select[Prime[Range[1000]], PrimeQ[# + 6] && PrimeQ[# + 12] && PrimeQ[# + 18] &] (* Vincenzo Librandi, Jul 15 2015 *)
(* The following program uses the AllTrue function from Mathematica version 10 *) Select[Prime[Range[3000]], AllTrue[# + {6, 12, 18}, PrimeQ] &] (* Harvey P. Dale, Jun 06 2017 *)
PROG
(Magma) [p: p in PrimesInInterval(2, 1000000) | forall{i: i in [ 6, 12, 18] | IsPrime(p+i)}]; // Vincenzo Librandi, Jul 15 2015
(PARI) main(size)=my(v=vector(size), i, r=1, p); for(i=1, size, while(1, p=prime(r); if(isprime(p+6)&&isprime(p+12)&&isprime(p+18), v[i]=p; r++; break, r++))); v \\ Anders Hellström, Jul 16 2015
CROSSREFS
KEYWORD
nonn
EXTENSIONS
Edited by N. J. A. Sloane, Aug 04 2009 following a suggestion from Daniel Forgues
STATUS
approved