This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A005267 M2248 #44 Aug 25 2024 11:23:48
%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) with a(0) = 3.
%C A005267 The next term is too large to include.
%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_, 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_, Apr 11 2005
%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.
%D A005267 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005267 Indranil Ghosh, <a href="/A005267/b005267.txt">Table of n, a(n) for n = 0..12</a>
%H A005267 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.
%H A005267 <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%F A005267 a(n) = -1 + a(0)a(1)...a(n-1).
%F A005267 a(n) = -1 + Product_{i<n} a(i). - _Henry Bottomley_, 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_, Apr 22 2007; _M. F. Hasler_, May 04 2007
%F A005267 For n>0, a(n) = a(0)^2 + a(1)^2 + ... + a(n-1)^2 - n - 6. - _Max Alekseyev_, Jun 19 2008
%o A005267 (PARI) a(n)=if(n<2,3*(n>=0)-(n>0),a(n-1)^2+a(n-1)-1)
%o A005267 (Python)
%o A005267 def a(n):
%o A005267 if n == 0: return 2
%o A005267 t = a(n-1)
%o A005267 l = t+1
%o A005267 u = t
%o A005267 return l * u - 1
%o A005267 print([a(n) for n in range(0, 8)]) # _Darío Clavijo_, Aug 24 2024
%Y A005267 Cf. A000058, A000289, A117805.
%K A005267 easy,nonn
%O A005267 0,1
%A A005267 _N. J. A. Sloane_