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%I #22 Oct 16 2023 11:27:43
%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 cross-referenced sequences. These are precisely the only unique primes (less than 10^50 at least) with this type of digit pattern: m 9's, m-1 0's and 1, in that order. (Also a(10) is a unique prime of period 120.)
%H Max Alekseyev, <a href="/A072848/b072848.txt">Table of n, a(n) for n = 1..87</a> (terms n=1..51 from Ray Chandler, n=52..81 from Daniel Suteu)
%H C. K. Caldwell, <a href="https://t5k.org/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
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