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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

Table of n, a(n) for n=0..8.

A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437.

Index entries for sequences of form a(n+1)=a(n)^2 + ...

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

N. J. A. Sloane

STATUS

approved

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