|
|
A370158
|
|
a(n) is the number of prime quadruples of the form {p, p+2, p+6, p+12} with p < 10^n.
|
|
0
|
|
|
0, 1, 4, 8, 24, 76, 313, 1644, 9397, 56734, 361386, 2417777, 16785520, 120150723, 882578840
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
These quadruples are adjacent twin/cousin/sexy prime pairs, and may consist of non-consecutive primes (see A086140).
|
|
LINKS
|
|
|
EXAMPLE
|
The third term, the count of quad primes < 10^2, is 4 and they are: (5,7,11,17), (11,13,17,23), (17,19,23,29), (41,43,47,53). The first term, the count of quad primes <10^0, is 0 since the smallest prime is 2.
|
|
PROG
|
(Perl) use ntheory ':all'; use bigint; sub a { my $count = () = sieve_prime_cluster(1, 10**$_[0], 2, 6, 12) }; $| = 1; for (0..12) { print(a($_), ", ") } # Daniel Suteu, Feb 23 2024
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|