1,2

This double modulo Ackermann function was inspired by the tiling problem given in "Elements of the Theory of Computation" which resembles an Ackermann recursion. The {a,b}->{5,6} was designed for the 10 X 10 output given to be active. Without the modulo this function is effectively limited to 4 X 4 in Mathematica by computation time.

http://mathworld.wolfram.com/AckermannFunction.html

Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 906, 2002.

" Elements of the Theory of Computation" by Harry R. Lewis and Christos H. Papadimitriou,Prentice-Hall, 1981, page 296 and 345

a(1, n) = Mod[n, 6]; a(m, 1) = a(m - 1, 2); a(m, n) = Mod[a(m - 1, a(m, n - 1) + 1), 5] aout(n,m)=AntidiagonalTransform(a(n,m))

{1},

{2, 2},

{3, 3, 3},

{0, 0, 4, 4},

{3, 3, 2, 0, 5},

{1, 1, 4, 4, 1, 0},

{1, 1, 3, 1, 1, 2, 1},

{1, 1, 1, 1, 0, 3, 3, 2},

{1, 1, 1, 1, 3, 3, 0, 4, 3},

{1, 1, 1, 1, 1, 1, 4, 2, 0, 4}

Clear[f] f[1, n_] := Mod[n, 6]; f[m_, 1] := f[m - 1, 2]; f[m_, n_] := Mod[f[m - 1, f[m, n - 1] + 1], 5]; 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]

Cf. A001695/M2352 and A014221.

Sequence in context: A127684 A036012 A084401 this_sequence A048485 A127714 A046918

Adjacent sequences: A131616 A131617 A131618 this_sequence A131620 A131621 A131622

nonn,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 02 2007