cp's OEIS Frontend

A350830 Number of prime 10-tuples (or decaplets) with initial member (A257127) between 10^(n-1) and 10^n.

%I A350830 #10 Apr 28 2022 13:14:43
%S A350830 0,1,0,0,0,0,0,0,0,1,4,15,81,357,1685,8256
%N A350830 Number of prime 10-tuples (or decaplets) with initial member (A257127) between 10^(n-1) and 10^n.
%C A350830 "Between 10^(n-1) and 10^n" is equivalent to saying "with n (decimal) digits".
%C A350830 A prime 10-tuple (or decaplet) is a sequence of 9 consecutive primes (p1, ..., p10) of minimum possible diameter p10 - p1 = 32.
%C A350830 Terms a(1)-a(16) computed from b-files a(1..10^4) for A027569 and A027570. Using Luhn's data (cf. LINKS) one can obtain a(18) and a(19).
%C A350830 So far the last term of all the decaplets has the same number of digits as the initial term.
%H A350830 Norman Luhn, <a href="http://www.pzktupel.de/smarchive.html">The big database of "The smallest prime k-tuplets"</a>, section "10-uplets": up to 10^20 as of March 2022.
%e A350830 a(2) = 1 because 11 is the only two-digit prime to start a prime decaplet, i.e., member of A257127.
%e A350830 a(n) = 0 for all other n < 10 because the next larger prime decaplet is made of 10-digit primes, A257127(2) = 9853497737 and successors.
%e A350830 a(10) = 1 because there is only one prime decaplet made of 10-digit primes.
%e A350830 a(11) = 4 because there are only four terms in A257127 (for indices n = 3..6) which have 11 digits.
%o A350830 (PARI) (D(v)=v[^1]-v[^-1])( [setsearch(A257127,10^n,1) | n<-[0..16]] ) \\ where A257127 is a vector of at least 10400 terms of that sequence.
%Y A350830 Cf. A257127 (initial members p of prime 9-tuples (p, ..., p+32)), A027569, A027570 (idem, specifically for each of the two possible patterns).
%Y A350830 Cf. A350825 - A350829: similar for quintuples, sextuples, septuples, octuples and 9-tuples.
%K A350830 nonn,base,hard,more
%O A350830 1,11
%A A350830 _M. F. Hasler_, Mar 01 2022