%I A003423 M4215
%S A003423 6,34,1154,1331714,1773462177794,3145168096065837266706434,
%T A003423 9892082352510403757550172975146702122837936996354
%N A003423 a(n) = a(n-1)^2 - 2.
%D A003423 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003423 E. Lucas, "Th\'eorie des Fonctions Num\'eriques Simplement P\'eriodiques, 
               II", Amer. J. Math., 1 (1878), 289-321.
%D A003423 L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 
               256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see 
               vol. 1, p. 376.
%D A003423 J. O. Shallit, An interesting continued fraction, Math. Mag., 48 (1975), 
               207-211.
%F A003423 a(n)=ceiling(c^(2^n)) where c=3+2*sqrt(2) is the largest root of x^2-6x+1=0. 
               - Benoit Cloitre, Dec 03, 2002
%F A003423 a(n)=(3+sqrt(8))^(2^n)+(3-sqrt(8))^(2^n). Sum_{n>=0} 1/( prod_{k=0..n} 
               a(k) ) = 3-sqrt(8). - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 
               11 2004
%F A003423 a(n)=2*A001601(n+1).
%F A003423 a(n-1)=Round[(1 + Sqrt[2])^(2^n)] [From Artur Jasinski (grafix(AT)csl.pl), 
               Sep 25 2008]
%t A003423 a[1] := 6; a[n_] := a[n - 1]^2 - 2; Table[a[n], {n, 1, 8}] - Stefan Steinerberger 
               (stefan.steinerberger(AT)gmail.com), Apr 11 2006
%t A003423 Table[Round[(1 + Sqrt[2])^(2^n)], {n, 1, 7}] [From Artur Jasinski (grafix(AT)csl.pl), 
               Sep 25 2008]
%o A003423 (PARI) a(n)=if(n<1, 6*(n==0), a(n-1)^2-2)
%Y A003423 Cf. A001566 (starting with 3), A003010 (starting with 4), A003487 (starting 
               with 5)
%Y A003423 Sequence in context: A062819 A092336 A161323 this_sequence A145000 A046025 
               A009583
%Y A003423 Adjacent sequences: A003420 A003421 A003422 this_sequence A003424 A003425 
               A003426
%K A003423 nonn,easy
%O A003423 0,1
%A A003423 N. J. A. Sloane (njas(AT)research.att.com).