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A001042
a(n) = a(n-1)^2 - a(n-2)^2.
(Formerly M0743 N0279)
3
1, 2, 3, 5, 16, 231, 53105, 2820087664, 7952894429824835871, 63248529811938901240357985099443351745, 4000376523371723941902615329287219027543200136435757892789536976747706216384
OFFSET
0,2
COMMENTS
The next term has 152 digits. - Franklin T. Adams-Watters, Jun 11 2009
REFERENCES
Archimedeans Problems Drive, Eureka, 27 (1964), 6.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..13
A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.
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!)
R. P. Loh, A. G. Shannon, A. F. Horadam, Divisibility Criteria and Sequence Generators Associated with Fermat Coefficients, Preprint, 1980.
FORMULA
a(n) ~ c^(2^n), where c = 1.1853051643868354640833201434870139866230288004895868726506278977814490371... . - Vaclav Kotesovec, Dec 17 2014
MATHEMATICA
RecurrenceTable[{a[0]==1, a[1]==2, a[n]==a[n-1]^2-a[n-2]^2}, a, {n, 0, 12}] (* Harvey P. Dale, Jan 11 2013 *)
PROG
(Haskell)
a001042 n = a001042_list !! n
a001042_list = 1 : 2 : zipWith (-) (tail xs) xs
where xs = map (^ 2) a001042_list
-- Reinhard Zumkeller, Dec 16 2013
CROSSREFS
Cf. A064236 (numbers of digits).
Sequence in context: A219339 A360695 A048112 * A214697 A379775 A035089
KEYWORD
nonn,nice,easy
EXTENSIONS
More terms from James A. Sellers, Sep 19 2000.
STATUS
approved