A003096 - OEIS (original) (raw)
A003096
a(n) = a(n-1)^2 - 1, a(0) = 2.
(Formerly M0894)
8
2, 3, 8, 63, 3968, 15745023, 247905749270528, 61457260521381894004129398783, 3776994870793005510047522464634252677140721938309041881088
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). 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
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, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)
MAPLE
a := proc(n) local k, v: v := 2: for k from 1 to n do v := v^2-1: od: v: end:
PROG
(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)