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A360469 Only k >= 0 such that, for every odd r > 0, A093179(n) divides the generalized Fermat number (A007117(n)^r)^(2^k) + 1.

%I A360469 #38 Jul 15 2023 06:01:39
%S A360469 3,3,5,3,7,7,9,8,11,11,13,10,15,15,17,16,19,19,21,19,23,23,25,24,27,
%T A360469 27,29,25,31,31,33,32,35,35,37,35,39,39,41,40,43,43,45,42,47,47,49,48,
%U A360469 51,51,53,51,55,55,57,56,59,59,61,56,63,63,65,64,67,67,69,67,71,71,73,72,75,75,77,74,79
%N A360469 Only k >= 0 such that, for every odd r > 0, A093179(n) divides the generalized Fermat number (A007117(n)^r)^(2^k) + 1.
%H A360469 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 A360469 a(n) = n - A007814(n + 2) (due to _Jinyuan Wang_).
%e A360469 A093179(5) = 641, A007117(5) = 5 and the only k >= 0 such that, for every odd r > 0, 641 divides the generalized Fermat number (5^r)^(2^k) + 1 is 5; so a(5) = 5.
%p A360469 a:=n->n-padic:-ordp(n+2,2):
%p A360469 seq(a(n), n=3..79);
%o A360469 (PARI) a(n) = n - valuation(n+2, 2);
%o A360469 vector(77,n,a(n+2)) \\ _Joerg Arndt_, Mar 03 2023
%Y A360469 Cf. A000215 (Fermat numbers), A007117, A007814 (dyadic valuation), A093179, A307843 (divisors of Fermat numbers).
%K A360469 nonn,easy
%O A360469 3,1
%A A360469 _Lorenzo Sauras Altuzarra_, Feb 27 2023