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%I #8 Mar 30 2012 17:34:21
%S 1,2,2,3,3,3,5,5,4,4,4,4,7,5,5,8,8,2,0,6,6,2,2,2,7,2,7,7,2,2,2,2,8,4,
%T 8,8,2,2,2,2,2,1,6,0,9,2,2,2,2,2,2,5,8,1,0,2,2,2,2,2,2,2,4,1,2,1,2,2,
%U 2,2,2,2,2,2,2,3,3,2,2,2,2,2,2,2,2,2,2,7,5,4,3,2,2,2,2,2,2,2,2,2,2,8,7,5,4,2,2,2,2,2,2,2,2,2,2,2,1,0,6
%N Square array read by antidiagonals: a(1,m) = m mod 10; a(n,1) = a(n-1,2); a(n,m) = a(n-1, a(n,m-1)+1) mod 9.
%C A double-modulus Ackermann recursion.
%D Harry R. Lewis and Christos H. Papadimitriou, Elements of the Theory of Computation, Prentice-Hall, 1981, pages 296 and 345
%D Wolfram, S., A New Kind of Science. Champaign, IL: Wolfram Media, p. 906, 2002.
%H Eric Weisstein, <a href="http://mathworld.wolfram.com/AckermannFunction.html">Ackermann Function</a>
%e 1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,...
%e 2,3,4,5,6,7,8,0,1,2,3,4,5,6,7,8,0,1,2,3,..
%e 3,5,7,0,2,4,6,8,1,3,5,7,0,2,4,6,8,1,3,5,...
%e 5,4,2,7,8,1,5,4,2,7,8,1,5,4,2,7,8,1,5,4,..
%e 4,8,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,...
%e 8,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,...
%p A131624 := proc(n,m) option remember; if n =1 then m mod 10 ; elif m = 1 then procname(n-1,2) ;else procname((n-1),1+procname(n,m-1)) mod 9 ; end if;end proc:
%t Clear[f] f[1, n_] := Mod[n, 10]; f[m_, 1] := f[m - 1, 2]; f[m_, n_] := Mod[f[m - 1, f[m, n - 1] + 1], 9]; a0 = Table[f[a, b], {a, 1, 10}, {b, 1, 10}]; ListDensityPlot[%,ColorFunction -> (Hue[2# ] &)]; Dimensions[a0]; (* antidiagonal transform*) c = Delete[Table[Reverse[Table[a0[[n, l - n]], {n, 1, l - 1}]], {l, 1, Dimensions[a0][[1]] + 1}], 1]; Flatten[c]
%Y Cf. A001695/M2352 and A014221.
%K nonn,tabl,easy
%O 1,2
%A _Roger L. Bagula_, Oct 02 2007
%E Edited by _N. J. A. Sloane_, Feb 02 2008
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