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%I A019434
%S A019434 3,5,17,257,65537
%N A019434 List of Fermat primes: primes of form 2^(2^k) + 1, for some k >= 0.
%D A019434 G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence 
               Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
%D A019434 R. K. Guy, Unsolved Problems in Number Theory, A3.
%H A019434 C. Banderier, <a href="http://algo.inria.fr/banderier/Recipro/node35.html">
               Pepin's Criterion For Fermat Numbers</a>
%H A019434 C. K. Caldwell, The Prime Glossary, <a href="http://primes.utm.edu/glossary/
               page.php?sort=Fermats">Fermat prime</a>
%H A019434 Wilfrid Keller, <a href="http://www.prothsearch.net/fermat.html">Prime 
               factors k.2^n + 1 of Fermat numbers F_m</a>
%H A019434 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PepinsTest.html">Link to a section of The World f Mathematics</a>
%H A019434 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FermatNumber.html">Fermat Number</a>
%H A019434 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FermatPrime.html">Fermat Prime</a>
%H A019434 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PepinsTest.html">Link to a section of The World of Mathematics</a>
%H A019434 Wikipedia, <a href="http://www.wikipedia.org/wiki/Fermat_prime">Fermat 
               prime</a>
%t A019434 Table[2^(2^n)+1, {n, 0, 4}] (from Vladimir Orlovsky (4vladimir(AT) gmail.com), 
               Apr 29 2008)
%o A019434 (PARI) for(i=0,99, isprime(2^2^i+1) & print1(2^2^i+1,", ")) \\ - M. F. 
               Hasler, Nov 21 2009
%Y A019434 Cf. A000215, A159611.
%Y A019434 Sequence in context: A023394 A056130 A078726 this_sequence A164307 A125045 
               A093179
%Y A019434 Adjacent sequences: A019431 A019432 A019433 this_sequence A019435 A019436 
               A019437
%K A019434 nonn,nice,new
%O A019434 1,1
%A A019434 N. J. A. Sloane (njas(AT)research.att.com), David W. Wilson (davidwwilson(AT)comcast.net)
%E A019434 It is conjectured that there are only 5 terms. Currently it has been 
               shown that 2^(2^k) + 1 is composite for 5<=k<=32 (see Eric Weisstein's 
               Fermat Primes link. - Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), 
               Sep 28 2008

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