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Search: id:A019434
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| A019434 |
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Fermat primes: primes of form 2^(2^n) + 1, n >= 0. |
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+0
90
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OFFSET
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0,1
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REFERENCES
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G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
R. K. Guy, Unsolved Problems in Number Theory, A3.
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LINKS
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C. Banderier, Pepin's Criterion For Fermat Numbers
C. K. Caldwell, The Prime Glossary, Fermat prime
Wilfrid Keller, Prime factors k.2^n + 1 of Fermat numbers F_m
Eric Weisstein's World of Mathematics, Link to a section of The World f Mathematics
Eric Weisstein's World of Mathematics, Fermat Number
Eric Weisstein's World of Mathematics, Fermat Prime
Wikipedia, Fermat prime
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MATHEMATICA
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Table[2^(2^n)+1, {n, 0, 4}] (from Vladimir Orlovsky (4vladimir(AT) gmail.com), Apr 29 2008)
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CROSSREFS
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Cf. A000215, A159611.
Sequence in context: A023394 A056130 A078726 this_sequence A164307 A125045 A093179
Adjacent sequences: A019431 A019432 A019433 this_sequence A019435 A019436 A019437
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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It is conjectured that there are only 5 terms. Currently it has been shown that 2^(2^n) + 1 is composite for 5<=n<=32 (see Eric Weisstein's Fermat Primes link. - Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Sep 28 2008
Offset corrected [so f_n = 2^(2^n) + 1 is prime for f_0 to f_4)] by Daniel Forgues (squid(AT)zensearch.com), Aug 14 2009
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