A370158 - OEIS

%I #39 Feb 29 2024 16:18:40

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

%T 882578840

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

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

%e 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.

%o (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

%Y Cf. A007530, A086140, A341267.

%K nonn,more

%O 0,3

%A _James S. DeArmon_, Feb 10 2024

%E a(8)-a(11) from _Hugo Pfoertner_, Feb 10 2024

%E a(12) from _Daniel Suteu_, Feb 23 2024

%E a(13)-a(14) from _Martin Ehrenstein_, Feb 29 2024