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%I A111635 #17 Dec 29 2019 09:49:38
%S A111635 2,5,17,257,65537,3512911982806776822251393039617,
%T A111635 4457915690803004131256192897205630962697827851093882159977969339137,
%U A111635 1638935311392320153195136107636665419978585455388636669548298482694235538906271958706896595665141002450684974003603106305516970574177405212679151205373697500164072550932748470956551681
%N A111635 Smallest prime of the form x^(2^n) + y^(2^n) where x,y are distinct integers.
%C A111635 Is this sequence defined for all n?
%C A111635 From _Jeppe Stig Nielsen_, Sep 16 2015: (Start)
%C A111635 Numbers of this form are sometimes called extended generalized Fermat numbers.
%C A111635 If we restrict ourselves to the case y=1, we get instead the sequence A123599, therefore a(n) <= A123599(n) for all n. Can this be an equality for some n > 4?
%C A111635 The formula x^(2^m) + y^(2^m) also gives the decreasing chain {A000040, A002313, A002645, A006686, A100266, A100267, ...} of subsets of the prime numbers if we drop the requirement that x != y and take all primes (not just the smallest one) with m greater than some lower bound.
%C A111635 (End)
%C A111635 For more terms (the values of max(x,y)), see A291944. - _Jeppe Stig Nielsen_, Dec 28 2019
%H A111635 Jeppe Stig Nielsen, <a href="/A111635/b111635.txt">Table of n, a(n) for n = 0..9</a>
%Y A111635 Cf. A019434, A100270, A123599, A291944.
%K A111635 nonn
%O A111635 0,1
%A A111635 _Max Alekseyev_, Aug 09 2005

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