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A003096
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a(n) = a(n-1)^2 - 1, a(0) = 2.
(Formerly M0894)
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8
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OFFSET
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0,1
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COMMENTS
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After a(0) = 2 and a(1) = 3, this can never be prime, since a(n) = (a(n-1) + 1) * (a(n-1) - 1). Each term is relatively prime to its successor. - Jonathan Vos Post, Jun 06 2008
Mensa (see Dutch link below) indicates high intelligence by offering a self test containing a number of problems, one of which is "Complete each series with the element that logically continues the series: 3968, 63, 8, 3". - David A. Corneth, May 19 2024
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REFERENCES
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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).
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LINKS
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FORMULA
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MAPLE
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a := proc(n) local k, v: v := 2: for k from 1 to n do v := v^2-1: od: v: end:
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MATHEMATICA
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PROG
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(PARI) a(n)=if(n<1, 2*(n==0), a(n-1)^2-1)
(Magma) [n le 1 select 2 else Self(n-1)^2 -1: n in [1..12]]; // G. C. Greubel, Oct 27 2022
(SageMath)
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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