A370158 a(n) is the number of prime quadruples of the form {p, p+2, p+6, p+12} with p < 10^n.

0, 1, 4, 8, 24, 76, 313, 1644, 9397, 56734, 361386, 2417777, 16785520, 120150723, 882578840

Offset

0,3

Comments

These quadruples are adjacent twin/cousin/sexy prime pairs, and may consist of non-consecutive primes (see A086140).

Links

Table of n, a(n) for n=0..14.

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

Cf. A007530, A086140, A341267.

Sequence in context: A334324 A010366 A222356 * A214201 A265185 A240530

Adjacent sequences: A370155 A370156 A370157 * A370159 A370160 A370161

Keyword

nonn,more

Author

James S. DeArmon, Feb 10 2024

Extensions

a(8)-a(11) from Hugo Pfoertner, Feb 10 2024

a(12) from Daniel Suteu, Feb 23 2024

a(13)-a(14) from Martin Ehrenstein, Feb 29 2024

Status

approved