Voozh

A005267

a(n) = -1 + a(0)*a(1)*...*a(n-1) with a(0) = 3.

3, 2, 5, 29, 869, 756029, 571580604869, 326704387862983487112029, 106735757048926752040856495274871386126283608869, 11392521832807516835658052968328096177131218666695418950023483907701862019030266123104859068029

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OFFSET

0,1

COMMENTS

The next term is too large to include.

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, 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, Apr 11 2005

REFERENCES

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.

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

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..12

R. K. Guy and R. Nowakowski, Discovering primes with Euclid, Research Paper No. 260 (Nov 1974), The University of Calgary Department of Mathematics, Statistics and Computing Science.

Index entries for sequences of form a(n+1)=a(n)^2 + ...

FORMULA

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

a(n) = -1 + Product_{i<n} a(i). - Henry Bottomley, 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, Apr 22 2007; M. F. Hasler, May 04 2007

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

PROG

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

(Python)

def a(n):

if n == 0: return 2