Search: id:A056993
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%I A056993
%S A056993 2,2,2,2,2,30,102,120,278,46,824,150,1534,30406,67234,70906,48594,62722
%N A056993 a(n) = smallest k >= 2 such that k^(2^n)+1 is prime.
%C A056993 Smallest base value yielding generalized Fermat primes. - Hugo Pfoertner 
               (hugo(AT)pfoertner.org), Jul 01 2003
%C A056993 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
%H A056993 Yves Gallot, <a href="http://perso.orange.fr/yves.gallot/primes/results.html">
               Generalized Fermat Prime Search</a>
%H A056993 Yves Gallot, <a href="http://perso.orange.fr/yves.gallot/primes/gfn.html">
               Generalized Fermat Prime Search</a>
%e A056993 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, ....
%t A056993 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)
%Y A056993 Cf. A006093, A005574, A000068, A006314, A006313, A006315, A006316, A056994, 
               A056995, A057465, A057002.
%Y A056993 Cf. A019434 (Fermat primes).
%Y A056993 Sequence in context: A095386 A060359 A029665 this_sequence A057331 A067089 
               A090872
%Y A056993 Adjacent sequences: A056990 A056991 A056992 this_sequence A056994 A056995 
               A056996
%K A056993 hard,nonn
%O A056993 0,1
%A A056993 Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 06 2000
%E A056993 1534 from Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 30 2000
%E A056993 62722 from Jeppe Stig Nielsen (sequence(AT)jeppesn.dk), Aug 07 2005

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