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
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Aug 04 2009 following a suggestion from Daniel Forgues
STATUS
approved