Search: id:A072848
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%I A072848
%S A072848 9901,99990001,999999000001,9999999900000001,39526741,3199044596370769,
%T A072848 4458192223320340849,75118313082913,59779577156334533866654838281,
%U A072848 100009999999899989999000000010001,2361000305507449,111994624258035614290513943330720125433979169
%N A072848 Largest prime factor of 10^(6*n) + 1.
%C A072848 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 A072848 C. K. Caldwell, <a href="http://primes.utm.edu/glossary/page.php?sort=UniquePrime">
               Unique Primes</a>
%e A072848 10^(6*4)+1 = 17 * 5882353 * 9999999900000001, so a(4) = 9999999900000001, 
               the largest prime factor.
%o A072848 (PARI) for(n=1,12,v=factor(10^(6*n)+1); print1(v[matsize(v)[1],1],","))
%Y A072848 Cf. A040017 (unique period primes), A051627 (associated periods).
%Y A072848 Sequence in context: A022199 A001230 A103810 this_sequence A145381 A031856 
               A031858
%Y A072848 Adjacent sequences: A072845 A072846 A072847 this_sequence A072849 A072850 
               A072851
%K A072848 nonn
%O A072848 1,1
%A A072848 Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 25 2002

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