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A003096 a(n) = a(n-1)^2 - 1.
(Formerly M0894)
7

%I M0894

%S 2,3,8,63,3968,15745023,247905749270528,61457260521381894004129398783,

%T 3776994870793005510047522464634252677140721938309041881088

%N a(n) = a(n-1)^2 - 1.

%C After a(0) = 2 and a(1) = 3, this can never be prime, since a(n) = (a(n-1)+1) * (a(n-1)-1). Yet each term is relatively prime to its successor. The initial value a(0) is arbitrary, however these properties hold for any integer a(0) > 1. - _Jonathan Vos Post_, Jun 06 2008

%D R. K. Guy, How to factor a number, Proc. 5th Manitoba Conf. Numerical Math., Congress. Num. 16 (1975), 49-89.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H A. V. Aho and N. J. A. Sloane, <a href="http://neilsloane.com/doc/doubly.html">Some doubly exponential sequences</a>, Fib. Quart., 11 (1973), 429-437.

%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>

%F a(n-1)=ceiling(c^(2^n)) where c=1.2955535361865325413981559700593353... - _Benoit Cloitre_, Nov 29 2002

%t a=2; lst={a}; Do[b=a^2-1; AppendTo[lst,b]; a=b, {n,10}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 28 2010 *)

%t NestList[#^2-1&,2,10] (* _Harvey P. Dale_, Nov 06 2011 *)

%o (PARI) a(n)=if(n<1,2*(n==0),a(n-1)^2-1)

%Y Cf. A139244.

%K nonn,easy,nice

%O 0,1

%A _N. J. A. Sloane_

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Last modified April 18 17:10 EDT 2019. Contains 322229 sequences. (Running on oeis4.)