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Search: id:A072848
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| A072848 |
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Largest prime factor of 10^(6*n) + 1. |
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+0
1
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| 9901, 99990001, 999999000001, 9999999900000001, 39526741, 3199044596370769, 4458192223320340849, 75118313082913, 59779577156334533866654838281, 100009999999899989999000000010001, 2361000305507449, 111994624258035614290513943330720125433979169
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.)
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LINKS
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C. K. Caldwell, Unique Primes
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EXAMPLE
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10^(6*4)+1 = 17 * 5882353 * 9999999900000001, so a(4) = 9999999900000001, the largest prime factor.
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PROGRAM
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(PARI) for(n=1, 12, v=factor(10^(6*n)+1); print1(v[matsize(v)[1], 1], ", "))
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CROSSREFS
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Cf. A040017 (unique period primes), A051627 (associated periods).
Sequence in context: A022199 A001230 A103810 this_sequence A145381 A031856 A031858
Adjacent sequences: A072845 A072846 A072847 this_sequence A072849 A072850 A072851
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KEYWORD
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nonn
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AUTHOR
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Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 25 2002
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