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.
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
t = a(n-1)
l = t+1
u = t
return l * u - 1
print([a(n) for n in range(0, 8)]) # Dar�o Clavijo, Aug 24 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved