Search: id:A005267
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%I A005267 M2248
%S A005267 3,2,5,29,869,756029,571580604869,326704387862983487112029,
%T A005267 106735757048926752040856495274871386126283608869,
%U A005267 11392521832807516835658052968328096177131218666695418950023483907701862019030266123104859068029
%N A005267 a(n) = -1 + a(0)a(1)...a(n-1) if n>0. a(0)=3.
%C A005267 An infinite coprime sequence defined by recursion. - Michael Somos Mar 
               14 2004
%C A005267 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 (benoit7848c(AT)orange.fr), Apr 
               02 2002
%C A005267 For positive n, a(n) has digital root 2 or 5 depending on whether n is 
               odd or even.(T.Koshy). - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Apr 11 2005
%D A005267 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005267 R. K. Guy and R. Nowakowski, ``Discovering primes with Euclid,'' Delta 
               (Waukesha), Vol. 5, pp. 49-63, 1975.
%D A005267 T. Koshy, "Intriguing Properties Of Three Related Number Sequences", 
               in Journal of Recreational Mathematics, Vol. 32(3) pp. 210-213, 2003-2004 
               Baywood NY.
%F A005267 a(n) = -1 + a(0)a(1)...a(n-1).
%F A005267 a(n) = -1 + product_{i<n} a(i). - Henry Bottomley (se16(AT)btinternet.com), 
               Jul 31 2000
%F A005267 a(n+1) = a(n)^2 + a(n) - 1 if n>1. a(0)=3, a(1)=2.
%F A005267 An induction shows that a(n+1) = A117805(n) - 1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Apr 22 2007; M. F. Hasler (maximilian.hasler(AT)gmail.com), May 04 
               2007.
%F A005267 For n>0, a(n) = a(0)^2 + a(1)^2 + ... + a(n-1)^2 - n - 6. - Max Alekseyev 
               (maxale(AT)gmail.com), Jun 19 2008
%o A005267 (PARI) a(n)=if(n<2,3*(n>=0)-(n>0),a(n-1)^2+a(n-1)-1)
%Y A005267 Cf. A000058, A000289, A117805.
%Y A005267 Sequence in context: A085973 A005265 A005266 this_sequence A016460 A097887 
               A019761
%Y A005267 Adjacent sequences: A005264 A005265 A005266 this_sequence A005268 A005269 
               A005270
%K A005267 easy,nonn
%O A005267 0,1
%A A005267 N. J. A. Sloane (njas(AT)research.att.com).
%E A005267 The next term is too large to include.

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