%I M0743 N0279 #32 Apr 07 2021 02:49:57
%S 1,2,3,5,16,231,53105,2820087664,7952894429824835871,
%T 63248529811938901240357985099443351745,
%U 4000376523371723941902615329287219027543200136435757892789536976747706216384
%N a(n) = a(n-1)^2 - a(n-2)^2.
%C The next term has 152 digits. - _Franklin T. Adams-Watters_, Jun 11 2009
%D Archimedeans Problems Drive, Eureka, 27 (1964), 6.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Reinhard Zumkeller, <a href="/A001042/b001042.txt">Table of n, a(n) for n = 0..13</a>
%H A. V. Aho and N. J. A. Sloane, <a href="https://www.fq.math.ca/Scanned/11-4/aho-a.pdf">Some doubly exponential sequences</a>, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437, <a href="http://neilsloane.com/doc/doubly.html">alternative link</a>.
%H R. K. Guy, <a href="/A002186/a002186.pdf">Letters to N. J. A. Sloane, June-August 1968</a>
%H R. P. Loh, A. G. Shannon, A. F. Horadam, <a href="/A000969/a000969.pdf">Divisibility Criteria and Sequence Generators Associated with Fermat Coefficients</a>, Preprint, 1980.
%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%F a(n) ~ c^(2^n), where c = 1.1853051643868354640833201434870139866230288004895868726506278977814490371... . - _Vaclav Kotesovec_, Dec 17 2014
%t 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 *)
%o (Haskell)
%o a001042 n = a001042_list !! n
%o a001042_list = 1 : 2 : zipWith (-) (tail xs) xs
%o where xs = map (^ 2) a001042_list
%o -- _Reinhard Zumkeller_, Dec 16 2013
%Y Cf. A001146, A000278, A000283, A058182, A007018.
%Y Cf. A064236 (numbers of digits).
%K nonn,nice,easy
%O 0,2
%A _N. J. A. Sloane_, _R. K. Guy_
%E More terms from _James A. Sellers_, Sep 19 2000