0,1

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

Let u(k), v(k) be defined by u(1)=1, v(1)=3, u(k+1)=v(k)-u(k), v(k+1)=u(k)v(k); then a(n)=v(2n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 02 2002

For positive n, a(n) has digital root 2 or 5 depending on whether n is odd or even.(T.Koshy). - Lekraj Beedassy (blekraj(AT)yahoo.com), Apr 11 2005

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

R. K. Guy and R. Nowakowski, ``Discovering primes with Euclid,'' Delta (Waukesha), Vol. 5, pp. 49-63, 1975.

T. Koshy, "Intriguing Properties Of Three Related Number Sequences", in Journal of Recreational Mathematics, Vol. 32(3) pp. 210-213, 2003-2004 Baywood NY.

a(n) = -1 + a(0)a(1)...a(n-1).

a(n) = -1 + product_{i<n} a(i). - Henry Bottomley (se16(AT)btinternet.com), Jul 31 2000

a(n+1) = a(n)^2 + a(n) - 1 if n>1. a(0)=3, a(1)=2.

An induction shows that a(n+1) = A117805(n) - 1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 22 2007; M. F. Hasler (maximilian.hasler(AT)gmail.com), May 04 2007.

For n>0, a(n) = a(0)^2 + a(1)^2 + ... + a(n-1)^2 - n - 6. - Max Alekseyev (maxale(AT)gmail.com), Jun 19 2008

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

Cf. A000058, A000289, A117805.

Sequence in context: A085973 A005265 A005266 this_sequence A016460 A097887 A019761

Adjacent sequences: A005264 A005265 A005266 this_sequence A005268 A005269 A005270

easy,nonn

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

The next term is too large to include.