login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

a(n) is the number of prime quadruples of the form {p, p+2, p+6, p+12} with p < 10^n.
0

%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