|
%I M2248 #37 Jun 29 2017 19:27:49
%S 3,2,5,29,869,756029,571580604869,326704387862983487112029,
%T 106735757048926752040856495274871386126283608869,
%U 11392521832807516835658052968328096177131218666695418950023483907701862019030266123104859068029
%N a(n) = -1 + a(0)a(1)...a(n-1) if n>0. a(0)=3.
%C The next term is too large to include.
%C An infinite coprime sequence defined by recursion. - _Michael Somos_, Mar 14 2004
%C 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
%C 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
%D R. K. Guy and R. Nowakowski, "Discovering primes with Euclid," Delta (Waukesha), Vol. 5, pp. 49-63, 1975.
%D T. Koshy, "Intriguing Properties Of Three Related Number Sequences", in Journal of Recreational Mathematics, Vol. 32(3) pp. 210-213, 2003-2004 Baywood NY.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Indranil Ghosh, <a href="/A005267/b005267.txt">Table of n, a(n) for n = 0..12</a>
%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%H R. K. Guy and R. Nowakowski, <a href="/A000945/a000945_5.pdf">Discovering primes with Euclid</a>, Research Paper No. 260 (Nov 1974), The University of Calgary Department of Mathematics, Statistics and Computing Science.
%F a(n) = -1 + a(0)a(1)...a(n-1).
%F a(n) = -1 + Product_{i<n} a(i). - _Henry Bottomley_, Jul 31 2000
%F a(n+1) = a(n)^2 + a(n) - 1 if n>1. a(0)=3, a(1)=2.
%F An induction shows that a(n+1) = A117805(n) - 1. - _R. J. Mathar_, Apr 22 2007; _M. F. Hasler_, May 04 2007
%F For n>0, a(n) = a(0)^2 + a(1)^2 + ... + a(n-1)^2 - n - 6. - _Max Alekseyev_, Jun 19 2008
%o (PARI) a(n)=if(n<2,3*(n>=0)-(n>0),a(n-1)^2+a(n-1)-1)
%Y Cf. A000058, A000289, A117805.
%K easy,nonn
%O 0,1
%A _N. J. A. Sloane_
| 