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a(0)=1, a(1)=1, a(n)=a(n-1)^a(n-2)+1.
4

%I #26 Sep 18 2015 15:58:11

%S 1,1,2,3,10,1001,1010045120210252210120045010002

%N a(0)=1, a(1)=1, a(n)=a(n-1)^a(n-2)+1.

%C a(7) has over 30000 digits.

%H <a href="/A184163/b184163.txt">Table of n, a(n) for n = 0..6</a>

%F a(n)=a(n-1)^a(n-2)+1

%e a(5)=a(4)^a(3)+1=(a(3)^a(2)+1)^(a(2)^a(1)+1)+1=((a(2)^a(1)+1)^(a(1)^a(0)+1)+1)^((a(1)^a(0)+1)+1)+1=(((a(1)^a(0)+1)+1)^(1+1)+1)^((1+1)+1)+1=(((1+1)+1)^2+1)^3+1=1001.

%o (Maxima)

%o a[0]:1$

%o a[1]:1$

%o a[n]:=a[n-1]^a[n-2]+1;

%o makelist(a[n],n,1,10); /* _Martin Ettl_, Oct 29 2012 */

%Y Cf. A218270, A218271, A218122.

%K nonn

%O 0,3

%A _Nico Brown_, Oct 24 2012