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A005267 a(n) = -1 + a(0)a(1)...a(n-1) if n>0. a(0)=3.
(Formerly M2248)
8
3, 2, 5, 29, 869, 756029, 571580604869, 326704387862983487112029, 106735757048926752040856495274871386126283608869, 11392521832807516835658052968328096177131218666695418950023483907701862019030266123104859068029 (list; graph; refs; listen; history; text; internal format)
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

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

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.

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)

CROSSREFS

Cf. A000058, A000289, A117805.

Sequence in context: A248243 A005265 A005266 * A209269 A244823 A286157

Adjacent sequences:  A005264 A005265 A005266 * A005268 A005269 A005270

KEYWORD

easy,nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 20 04:05 EST 2017. Contains 294959 sequences.