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 A093179 Smallest factor of the n-th Fermat number F(n) = 2^(2^n) + 1. 10
 3, 5, 17, 257, 65537, 641, 274177, 59649589127497217, 1238926361552897, 2424833, 45592577, 319489, 114689, 2710954639361, 116928085873074369829035993834596371340386703423373313, 1214251009, 825753601, 31065037602817, 13631489, 70525124609 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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 LINKS Ivars Peterson, Cracking Fermat Numbers Eric Weisstein's World of Mathematics, Fermat Number FORMULA a(n) = A007117(n)*2^(n+2) + 1 for n >= 2. - Jianing Song, Mar 02 2021 EXAMPLE 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. MATHEMATICA Table[With[{k = 2^n}, FactorInteger[2^k + 1]][[1, 1]], {n, 0, 15, 1}] (* Vincenzo Librandi, Jul 23 2013 *) PROG (PARI) g(n)=for(x=9, n, y=Vec(ifactor(2^(2^x)+1)); print1(y[1]", ")) \\ Cino Hilliard, Jul 04 2007 CROSSREFS Cf. A000051, A070592, A007117. Leading entries in triangle A050922. Sequence in context: A019434 A164307 A125045 * A067387 A050922 A260476 Adjacent sequences:  A093176 A093177 A093178 * A093180 A093181 A093182 KEYWORD nonn,hard AUTHOR Eric W. Weisstein, Mar 27 2004 EXTENSIONS Edited by N. J. A. Sloane, Jul 02 2008 at the suggestion of R. J. Mathar Added a(14)-a(15), Jeppe Stig Nielsen, Feb 11 2010 a(16)-a(19) added based on terms of A007117 by Jianing Song, Mar 02 2021 STATUS approved

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Last modified April 17 12:58 EDT 2021. Contains 343063 sequences. (Running on oeis4.)