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A093179 Smallest factor of the n-th Fermat number F(n) = 2^(2^n)+1. 9
3, 5, 17, 257, 65537, 641, 274177, 59649589127497217, 1238926361552897, 2424833, 45592577, 319489, 114689, 2710954639361, 116928085873074369829035993834596371340386703423373313, 1214251009 (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

Table of n, a(n) for n=0..15.

Ivars Peterson, Cracking Fermat Numbers

Wilfrid Keller, Prime factors  k ยท 2^n + 1  of Fermat numbers  F_m and complete factoring status

Eric Weisstein's World of Mathematics, Fermat Number

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.

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

STATUS

approved

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Last modified April 8 11:18 EDT 2020. Contains 333313 sequences. (Running on oeis4.)