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A005267
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a(n) = -1 + a(0)*a(1)*...*a(n-1) with a(0) = 3.
(Formerly M2248)
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8
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3, 2, 5, 29, 869, 756029, 571580604869, 326704387862983487112029, 106735757048926752040856495274871386126283608869, 11392521832807516835658052968328096177131218666695418950023483907701862019030266123104859068029
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listen;
history;
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OFFSET
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0,1
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COMMENTS
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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
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REFERENCES
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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).
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LINKS
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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.
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FORMULA
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a(n) = -1 + a(0)a(1)...a(n-1).
a(n+1) = a(n)^2 + a(n) - 1 if n>1. a(0)=3, a(1)=2.
For n>0, a(n) = a(0)^2 + a(1)^2 + ... + a(n-1)^2 - n - 6. - Max Alekseyev, Jun 19 2008
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn,changed
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AUTHOR
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STATUS
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approved
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