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Search: id:A102050
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| A102050 |
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a(n) = 1 if 10^(2^n)+1 is prime, otherwise smallest prime factor of 10^(2^n)+1. |
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+0
2
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| 1, 1, 73, 17, 353, 19841, 1265011073, 257, 10753, 1514497, 1856104284667693057, 106907803649, 458924033
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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10^(2^13)+1 and 10^(2^14)+1 are composite, but no prime factors are known. The smallest known prime factors of 10^(2^15)+1 to 10^(2^18)+1 are 65537, 8257537, 175636481, 639631361.
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LINKS
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Wilfrid Keller, Prime factors of generalized Fermat numbers Fm(10) and complete factoring status
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EXAMPLE
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10^(2^4)+1 = 10000000000000001 = 353*449*641*1409*69857, hence a(4) = 353.
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PROGRAM
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(PARI) for(k=0, 8, fac=factor(10^(2^k)+1); print1(if(matsize(fac)[1]==1, 1, fac[1, 1]), ", "))
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CROSSREFS
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Cf. A000533, A002275.
Sequence in context: A113889 A099191 A051325 this_sequence A057446 A033393 A153646
Adjacent sequences: A102047 A102048 A102049 this_sequence A102051 A102052 A102053
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KEYWORD
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nonn,hard,more
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004
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