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A093179
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Smallest prime factor of the n-th Fermat number F(n) = 2^(2^n) + 1.
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12
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3, 5, 17, 257, 65537, 641, 274177, 59649589127497217, 1238926361552897, 2424833, 45592577, 319489, 114689, 2710954639361, 116928085873074369829035993834596371340386703423373313, 1214251009, 825753601, 31065037602817, 13631489, 70525124609
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OFFSET
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0,1
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COMMENTS
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a(14) might need to be corrected if F(14) turns out to have a smaller factor than 116928085873074369829035993834596371340386703423373313. F(20) is composite, but no explicit factor is known. - Jeppe Stig Nielsen, Feb 11 2010
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LINKS
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FORMULA
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EXAMPLE
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F(0) = 2^(2^0) + 1 = 3, prime.
F(5) = 2^(2^5) + 1 = 4294967297 = 641*6700417.
So 3 as the 0th entry and 641 is the 5th term.
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MATHEMATICA
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Table[With[{k = 2^n}, FactorInteger[2^k + 1]][[1, 1]], {n, 0, 15, 1}] (* Vincenzo Librandi, Jul 23 2013 *)
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PROG
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(PARI) g(n)=for(x=9, n, y=Vec(ifactor(2^(2^x)+1)); print1(y[1]", ")) \\ Cino Hilliard, Jul 04 2007
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CROSSREFS
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Leading entries in triangle A050922.
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KEYWORD
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nonn,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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