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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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5
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1, 1, 1, 1, 1, 8, 95, 31, 85, 59, 1078, 754, 311, 3508, 1828, 49957, 22844
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OFFSET
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0,6
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COMMENTS
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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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LINKS
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FORMULA
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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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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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