0,2

An infinite coprime sequence defined by recursion. - Michael Somos Mar 14 2004

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

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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. 397.

E. Lucas, Nouveaux theoremes d'arithmetique superieure, Comptes Rend., 83 (1876), 1286-1288.

M. Mendes France and A. J. van der Poorten, From geometry to Euler identities, Theoret. Comput. Sci., 65 (1989), 213-220.

J. O. Shallit, Predictable regular continued cotangent expansions. J. Res. Nat. Bur. Standards Sect. B 80B (1976), no. 2, 285-290.

a(n) = Fib(3^n)/Fib(3^(n-1)) - Henry Bottomley (se16(AT)btinternet.com), Jul 10 2001

a(n+1) = 5*(f(n))^2 - 3, where f(n) = Fib(3^n) = product of first n entries. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 16 2003

Contribution from Artur Jasinski (grafix(AT)csl.pl), Oct 05 2008: (Start)

a(n+2)=(G^(3^(n + 1)) - (1 - G)^(3^(n + 1)))/((G^(3^n)) - (1 - G)^(3^n)) where G = (1 + Sqrt[5])/2

a(n+2)=A045529(n+1)/A045529(n) (End)

G = (1 + Sqrt[5])/2; Table[Expand[(G^(3^(n + 1)) - (1 - G)^(3^(n + 1)))/Sqrt[5]]/Expand[((G^(3^n)) - (1 - G)^(3^n))/Sqrt[5]], {n, 1, 7}] [From Artur Jasinski (grafix(AT)csl.pl), Oct 05 2008]

(PARI) a(n)=if(n<2, max(0, n+1), a(n-1)^3+3*a(n-1)^2-3)

Cf. A000045, A001566.

Cf. A045529.

Sequence in context: A122054 A092415 A060353 this_sequence A122207 A003819 A078624

Adjacent sequences: A002811 A002812 A002813 this_sequence A002815 A002816 A002817

nonn,easy,nice

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