Search: id:A003096
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%I A003096 M0894
%S A003096 2,3,8,63,3968,15745023,247905749270528,61457260521381894004129398783,
%T A003096 3776994870793005510047522464634252677140721938309041881088
%N A003096 a(n) = a(n-1)^2 - 1.
%C A003096 After a(0) = 2 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 (jvospost3(AT)gmail.com), Jun 06 2008
%D A003096 R. K. Guy, How to factor a number, Proc. 5th Manitoba Conf. Numerical 
               Math., Congress. Num. 16 (1975), 49-89.
%D A003096 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A003096 A. V. Aho and N. J. A. Sloane, <a href="http://www.research.att.com/~njas/
               doc/doubly.html">Some doubly exponential sequences</a>, Fib. Quart., 
               11 (1973), 429-437.
%H A003096 <a href="Sindx_Aa.html#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 
               + ...</a>
%F A003096 a(n-1)=ceiling(c^(2^n)) where c=1.2955535361865325413981559700593353... 
               - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 29 2002
%o A003096 (PARI) a(n)=if(n<1,2*(n==0),a(n-1)^2-1)
%Y A003096 Sequence in context: A042365 A072043 A095203 this_sequence A042815 A005008 
               A079938
%Y A003096 Adjacent sequences: A003093 A003094 A003095 this_sequence A003097 A003098 
               A003099
%K A003096 nonn,easy,nice
%O A003096 0,1
%A A003096 N. J. A. Sloane (njas(AT)research.att.com).

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