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%I #30 Dec 27 2022 16:54:12
%S 0,0,0,0,0,23,46,73,206,491,999,2030,4080,8151
%N a(n) is the minimum integer k such that the smallest prime factor of the n-th Fermat number exceeds 2^(2^n - k).
%C 2^(2^n - a(n)) < A093179(n).
%C Conjecture: the dyadic valuation of A093179(n) - 1 does not exceed 2^n - a(n).
%C a(14) is probably equal to 16208; a(15) to a(19) are 32738, 65507, 131028, 262121, 524252; a(20) is unknown; a(21) to a(23) are 2097110, 4194189, 8388581; a(24) is unknown.
%H Lorenzo Sauras-Altuzarra, <a href="https://doi.org/10.26493/2590-9770.1473.ec5">Some properties of the factors of Fermat numbers</a>, Art Discrete Appl. Math. (2022).
%F Conjecture: a(n) ~ 2^n as n -> oo.
%e For n=5, the smallest prime factor of F(5) = 2^(2^5) + 1 is 641 and it falls between 2^(2^5 - 23) = 512 < 641 < 1024 = 2^(2^5 - 22) so that a(5) = 23.
%Y Cf. A000215, A093179.
%K nonn,more
%O 0,6
%A _Lorenzo Sauras Altuzarra_, Nov 26 2022
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