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Search: id:A056993
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| A056993 |
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a(n) = smallest k >= 2 such that k^(2^n)+1 is prime. |
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+0
9
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| 2, 2, 2, 2, 2, 30, 102, 120, 278, 46, 824, 150, 1534, 30406, 67234, 70906, 48594, 62722
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Smallest base value yielding generalized Fermat primes. - Hugo Pfoertner (hugo(AT)pfoertner.org), Jul 01 2003
The first 5 terms correspond with the known (ordinary) Fermat primes. A probable candidate for the next entry is 62722^131072+1, discovered by Michael Angel in 2003. It has 628808 decimal digits. - Hugo Pfoertner (hugo(AT)pfoertner.org), Jul 01 2003
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LINKS
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Yves Gallot, Generalized Fermat Prime Search
Yves Gallot, Generalized Fermat Prime Search
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EXAMPLE
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The primes are 2^(2^0)+1=3, 2^(2^1)+1=5, 2^(2^2)+1=17, 2^(2^3)+1=257, 2^(2^4)+1=65537, 30^(2^5)+1, 102^(2^6)+1, ....
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MATHEMATICA
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f[n_] := (p = 2^n; k = 2; While[cp = k^p + 1; !PrimeQ@cp, k++ ]; k); Do[ Print[{n, f@n}], {n, 0, 17}] (from Lei Zhou (lzhou5(AT)emory.edu), Feb 21 2005)
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CROSSREFS
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Cf. A006093, A005574, A000068, A006314, A006313, A006315, A006316, A056994, A056995, A057465, A057002.
Cf. A019434 (Fermat primes).
Sequence in context: A095386 A060359 A029665 this_sequence A057331 A067089 A090872
Adjacent sequences: A056990 A056991 A056992 this_sequence A056994 A056995 A056996
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KEYWORD
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hard,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 06 2000
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EXTENSIONS
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1534 from Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 30 2000
62722 from Jeppe Stig Nielsen (sequence(AT)jeppesn.dk), Aug 07 2005
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