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A283051 Positive integers n such that none of the primes of the form k*2^n + 1 (with k odd) divide any Fermat number F(m) = 2^(2^m) + 1, m >= 0.

%I A283051 #5 Feb 16 2025 08:33:42
%S A283051 3,5,6,10
%N A283051 Positive integers n such that none of the primes of the form k*2^n + 1 (with k odd) divide any Fermat number F(m) = 2^(2^m) + 1, m >= 0.
%C A283051 Conjecture: sequence is infinite.
%C A283051 a(5) >= 18.
%H A283051 Proth Search Page, <a href="http://www.prothsearch.com/fermat.html">Prime factors of Fermat numbers</a>
%H A283051 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FermatNumber.html">Fermat Number</a>
%Y A283051 Cf. A019434, A023394, A228845, A228846, A229857, A231203.
%K A283051 nonn,hard,more
%O A283051 1,1
%A A283051 _Arkadiusz Wesolowski_, Feb 27 2017