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 A003096 a(n) = a(n-1)^2 - 1. (Formerly M0894) 7
 2, 3, 8, 63, 3968, 15745023, 247905749270528, 61457260521381894004129398783, 3776994870793005510047522464634252677140721938309041881088 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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 REFERENCES R. K. Guy, How to factor a number, Proc. 5th Manitoba Conf. Numerical Math., Congress. Num. 16 (1975), 49-89. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437. FORMULA a(n-1)=ceiling(c^(2^n)) where c=1.2955535361865325413981559700593353... - Benoit Cloitre, Nov 29 2002 MATHEMATICA a=2; lst={a}; Do[b=a^2-1; AppendTo[lst, b]; a=b, {n, 10}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 28 2010 *) NestList[#^2-1&, 2, 10] (* Harvey P. Dale, Nov 06 2011 *) PROG (PARI) a(n)=if(n<1, 2*(n==0), a(n-1)^2-1) CROSSREFS Cf. A139244. Sequence in context: A160634 A072043 A095203 * A042815 A191353 A319218 Adjacent sequences:  A003093 A003094 A003095 * A003097 A003098 A003099 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified March 21 18:59 EDT 2019. Contains 321382 sequences. (Running on oeis4.)