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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
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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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Table of n, a(n) for n=0..15.
T. D. Noe, Table of generalized Fermat primes of the form (k+1)^2^m + k^2^m
Anders Björn and Hans Riesel, Factors of generalized Fermat numbers, Math. Comp. 67 (1998), no. 221, pp. 441-446.
Eric Weisstein's World of Mathematics, Generalized Fermat Number
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FORMULA
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a(n) = A253633(n) - 1.
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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, A153504, A152913, A194185, A253633.
Sequence in context: A010565 A299002 A299669 * A297857 A298092 A298054
Adjacent sequences: A080205 A080206 A080207 * 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, Feb 10 2003
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EXTENSIONS
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a(14)-a(15) from Jeppe Stig Nielsen, Nov 27 2020
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STATUS
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approved
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