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A058220
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Ultra-useful primes: smallest k such that 2^(2^n) - k is prime.
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7
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1, 3, 5, 15, 5, 59, 159, 189, 569, 105, 1557, 2549, 2439, 13797, 25353, 5627, 24317, 231425, 164073
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OFFSET
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1,2
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COMMENTS
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2^(2^16) - 5627 was found by Joel Levy in Feb 2004. - Donovan Johnson, Sep 13 2008
Corresponding numbers to entries a(1) to a(12) are proven primes, higher terms are probable primes. - Matthias Baur, Mar 17 2020
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LINKS
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FORMULA
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EXAMPLE
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For n = 3, we see that 2^(2^3) = 2^8 = 256, which is clearly not prime.
256 - 1 = 255 = 3 * 5 * 17, so a(3) is not 1.
256 - 2 = 254 = 2 * 127, so a(3) is not 2 either.
256 - 3 = 253 = 11 * 23, so a(3) is not 3 either.
256 - 5 = 251, which is prime, so a(3) = 5.
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MATHEMATICA
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ultraUseful[n_] := Module[{x = 2^(2^n)}, x - NextPrime[x, -1]]; Array[ultraUseful, 17] (* Harvey P. Dale, Jun 04 2011 *)
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CROSSREFS
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KEYWORD
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nonn,hard,nice,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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