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Search: id:A080208
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| A080208 |
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a(n) is the least k such that the generalized Fermat number (k+1)^(2^n) + k^(2^n) is prime. |
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4
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| 1, 1, 1, 1, 1, 8, 95, 31, 85, 59, 1078, 754, 311, 3508
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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The first five terms correspond to the five known Fermat primes. The sequence A078902 lists some of the generalized Fermat primes. Bjorn and Riesel examined generalized Fermat numbers for k <= 11 and n <= 999. The sequence A080134 lists the conjectured number of primes for each k.
For n >= 10, a(n) yields a probable prime. a(13) was found by Henri Lifchitz. It is known that a(14) > 1000.
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REFERENCES
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A. Bjorn and H. Riesel, "Factors of generalized Fermat numbers," Math. Comp., 67 (1998) 441-446.
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LINKS
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T. D. Noe, Table of generalized Fermat primes of the form (k+1)^2^m + k^2^m
Eric Weisstein's World of Mathematics, Generalized Fermat Number
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EXAMPLE
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a(5) = 8 because (k+1)^32 + k^32 is prime for k = 8 and composite for k < 8.
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CROSSREFS
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Cf. A019434, A078902, A080134.
Sequence in context: A121161 A098269 A010565 this_sequence A099298 A003775 A121785
Adjacent sequences: A080205 A080206 A080207 this_sequence A080209 A080210 A080211
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KEYWORD
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hard,more,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Feb 10 2003
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