A360469 - OEIS

%I #38 Jul 15 2023 06:01:39

%S 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 27,29,25,31,31,33,32,35,35,37,35,39,39,41,40,43,43,45,42,47,47,49,48,

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

%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 a(n) = n - A007814(n + 2) (due to _Jinyuan Wang_).

%e 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 a:=n->n-padic:-ordp(n+2,2):

%p seq(a(n), n=3..79);

%o (PARI) a(n) = n - valuation(n+2, 2);

%o vector(77,n,a(n+2)) \\ _Joerg Arndt_, Mar 03 2023

%Y Cf. A000215 (Fermat numbers), A007117, A007814 (dyadic valuation), A093179, A307843 (divisors of Fermat numbers).

%K nonn,easy

%O 3,1

%A _Lorenzo Sauras Altuzarra_, Feb 27 2023