A001042 a(n) = a(n-1)^2 - a(n-2)^2. (Formerly M0743 N0279)

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, alternative link.

R. K. Guy, Letters to N. J. A. Sloane, June-August 1968

R. P. Loh, A. G. Shannon, A. F. Horadam, Divisibility Criteria and Sequence Generators Associated with Fermat Coefficients, Preprint, 1980.

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

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. A001146, A000278, A000283, A058182, A007018.

Cf. A064236 (numbers of digits).

Sequence in context: A219339 A360695 A048112 * A214697 A035089 A045313

Adjacent sequences: A001039 A001040 A001041 * A001043 A001044 A001045

Keyword

nonn,nice,easy

Author

N. J. A. Sloane, R. K. Guy

Extensions

More terms from James A. Sellers, Sep 19 2000

Status

approved