0,1

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

E. Lucas, "Th\'eorie des Fonctions Num\'eriques Simplement P\'eriodiques, II", Amer. J. Math., 1 (1878), 289-321.

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.

J. O. Shallit, An interesting continued fraction, Math. Mag., 48 (1975), 207-211.

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

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

a(n)=2*A001601(n+1).

a(n-1)=Round[(1 + Sqrt[2])^(2^n)] [From Artur Jasinski (grafix(AT)csl.pl), Sep 25 2008]

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

Table[Round[(1 + Sqrt[2])^(2^n)], {n, 1, 7}] [From Artur Jasinski (grafix(AT)csl.pl), Sep 25 2008]

(PARI) a(n)=if(n<1, 6*(n==0), a(n-1)^2-2)

Cf. A001566 (starting with 3), A003010 (starting with 4), A003487 (starting with 5)

Sequence in context: A062819 A092336 A161323 this_sequence A145000 A046025 A009583

Adjacent sequences: A003420 A003421 A003422 this_sequence A003424 A003425 A003426

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).