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%I #17 May 31 2022 12:55:10
%S 4,28,19684,7625597484988,443426488243037769948249630619149892804,
%T 87189642485960958202911070585860771696964072404731750085525219437990967093723439943475549906831683116791055225665628
%N Base-3 Fermat numbers: 3^(3^n) + 1.
%C Apparently discovered (with arbitrary base) by Gottschalk in 1938 and independently by Ferentinou-Nicolacopoulou in 1963. - _Charles R Greathouse IV_, Jul 05 2011
%C a(n) divides a(n+1). a(n+1)/a(n) = (3^(3^(n+1)) + 1)/(3^(3^n) + 1) = 1 - 3^(3^n) + 9^(3^n) = A002061(3^(3^n)) = A129291(n) = {7, 703, 387400807, 58149737003032434092905183, ...}.
%D J. Ferentinou-Nicolacopoulou, "Une propriété des diviseurs du nombre r^(r^m)+1. Applications au dernier théorème de Fermat." Bulletin Société Mathématique de Grèce 4:1 (1963), pp. 121-126.
%H Eugen Gottschalk, <a href="http://dx.doi.org/10.1007/BF01448935">Zum Fermatschen Problem</a>, Mathematische Annalen 115 (1934), pp. 157-158.
%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) = 3^(3^n) + 1. a(n) = A055777(n) + 1.
%t Table[3^3^n+1,{n,0,6}]
%o (PARI) a(n)=3^(3^n)+1 \\ _Charles R Greathouse IV_, Jul 05 2011
%Y Cf. A000215 (Fermat numbers: 2^(2^n) + 1).
%Y Cf. A055777 (3^(3^n)).
%Y Cf. A129291 (A129290(n+1) / A129290(n)).
%Y Cf. A002061 (central polygonal numbers: n^2 - n + 1).
%K nonn
%O 0,1
%A _Alexander Adamchuk_, Apr 08 2007
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