%I A143797
%S A143797 1,2,2,3,3,0,4,4,2,1,5,5,4,2,1,6,6,6,4,2,1,7,7,8,8,4,2,1,8,8,10,16,16,
               4,
%T A143797 2,1,9,9,12,32,65536,65536,4,2,1,10,10,14,64
%N A143797 Ackermann-Buck function, defined recursively by A(0,n) = n+1, A(1,0) 
               = 2, A(2,0) = 0, A(n+3,0) = 1, A(m+1,n+1) = A(m,A(m+1,n)) for any 
               nonnegative integers n, m. Table read by antidiagonals, the second 
               term being A(0,1).
%C A143797 The next term is 2^^5 = 2^2^2^2^2 = 2^65536.
%C A143797 This is a computable function that is not primitive recursive.
%D A143797 W. Ackermann, Zum Hilbertschen Aufbau der reellen Zahlen, Math. Ann. 
               99 (1928), 118-133.
%D A143797 R. C. Buck, Mathematical induction and recursive definitions, Amer. Math. 
               Monthly, 70 (1963), 128-135.
%D A143797 R. Peter, Rekursive Funktionen in der Komputer-Theorie. Budapest: Akad. 
               Kiado, 1951.
%H A143797 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ackermann_function">
               Ackermann function</a>.
%H A143797 E. Weisstein, Mathworld, <a href="http://mathworld.wolfram.com/AckermannFunction.html">
               Ackermann function</a>.
%F A143797 T(n,0) = 1 if n>=3.
%F A143797 T(n,1) = 2 if n>=2.
%F A143797 T(n,2) = 4 if n>=1.
%F A143797 T(1,n) = 2+n.
%F A143797 T(2,n) = 2*n.
%F A143797 T(3,n) = 2^n.
%F A143797 T(4,n) = 2^^n (a power tower of n two's) = A014221(n+1).
%Y A143797 A001695(n)=A(n, n). Cf. A143796.
%Y A143797 Sequence in context: A127009 A164089 A068460 this_sequence A079729 A071859 
               A105899
%Y A143797 Adjacent sequences: A143794 A143795 A143796 this_sequence A143798 A143799 
               A143800
%K A143797 nonn,tabl
%O A143797 0,2
%A A143797 Benoit Jubin (benoit_jubin(AT)yahoo.fr), Sep 01 2008