%I
%S 9901,99990001,999999000001,9999999900000001,39526741,
%T 3199044596370769,4458192223320340849,75118313082913,
%U 59779577156334533866654838281,100009999999899989999000000010001,2361000305507449,111994624258035614290513943330720125433979169
%N Largest prime factor of 10^(6*n) + 1.
%C According to the link, there are only 18 "unique primes" below 10^50. The first four terms above are each unique primes, of periods 12, 24, 36 and 48, respectively, according to Caldwell and the crossreferenced sequences. These are precisely the only unique primes (less than 10^50 at least) with this type of digit pattern: m 9's, m1 0's and 1, in that order. (Also a(10) is a unique prime of period 120.)
%H Ray Chandler, <a href="/A072848/b072848.txt">Table of n, a(n) for n = 1..51</a>
%H C. K. Caldwell, <a href="http://primes.utm.edu/glossary/page.php?sort=UniquePrime">Unique Primes</a>
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/repunit/10001.htm">Factorizations of 100...001</a>.
%F a(n) = A003021(6n) = A006530(A062397(6n)).  _Ray Chandler_, May 11 2017
%e 10^(6*4)+1 = 17 * 5882353 * 9999999900000001, so a(4) = 9999999900000001, the largest prime factor.
%o (PARI) for(n=1,12,v=factor(10^(6*n)+1); print1(v[matsize(v)[1],1],","))
%Y Cf. A040017 (unique period primes), A051627 (associated periods).
%Y Cf. A003021, A006530, A062397.
%K nonn
%O 1,1
%A _Rick L. Shepherd_, Jul 25 2002
