OFFSET
1,2
COMMENTS
A "prime quadruplet" is a set of four primes {p, p+2, p+6, p+8}.
a(1) = 0 rather than 1 because the quadruple {2,3,5,7} does not have the official form.
LINKS
Thomas R. Nicely, Enumeration of the prime quadruplets to 1e16.
Thomas R. Nicely, Enumeration to 1.6e15 of the prime quadruplets.
Jonathan P. Sorenson, Jonathan Webster, Two Algorithms to Find Primes in Patterns, arXiv:1807.08777 [math.NT], 2018.
Eric Weisstein's World of Mathematics, Prime Quadruplet.
EXAMPLE
a(2) = 2 because there are two prime quadruplets with largest member less than 10^2, namely {5, 7, 11, 13} and {11, 13, 17, 19}.
a(3) = 5 because, in addition to the prime quadruplets mentioned above, below 10^3 we also have {101, 103, 107, 109}, {191, 193, 197, 199} and {821, 823, 827, 829}.
MATHEMATICA
c = 1; Do[ Do[ If[ PrimeQ[ n ] && PrimeQ[ n + 2 ] && PrimeQ[ n + 6 ] && PrimeQ[ n + 8 ], c++ ], {n, 10^n + 1, 10^(n + 1), 10} ]; Print[ c ], {n, 1, 15} ] (* Weisstein *)
(* First run program for A090258 *) Table[Length[Select[A090258, # < 10^n &]], {n, 5}] (* Alonso del Arte, Aug 12 2012 *)
CROSSREFS
KEYWORD
nonn,nice,hard
AUTHOR
EXTENSIONS
a(16) (from Nicely link) added by Donovan Johnson, Jan 11 2011
a(17) added by Jonathan Webster, Jun 26 2018
a(1) changed to 0 at the suggestion of Harvey P. Dale. - N. J. A. Sloane, Sep 25 2019
STATUS
approved