A131624 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.

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, 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, 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

Offset

1,2

Comments

A double-modulus Ackermann recursion.

References

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

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

Links

Table of n, a(n) for n=1..119.

Eric Weisstein, Ackermann Function

Example

1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,...
2,3,4,5,6,7,8,0,1,2,3,4,5,6,7,8,0,1,2,3,..
3,5,7,0,2,4,6,8,1,3,5,7,0,2,4,6,8,1,3,5,...
5,4,2,7,8,1,5,4,2,7,8,1,5,4,2,7,8,1,5,4,..
4,8,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,...
8,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,...

Maple

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:

Mathematica

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]

Crossrefs

Cf. A001695/M2352 and A014221.

Sequence in context: A318350 A127332 A087826 * A165077 A165079 A175944

Adjacent sequences: A131621 A131622 A131623 * A131625 A131626 A131627

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, Oct 02 2007

Extensions

Edited by N. J. A. Sloane, Feb 02 2008

Status

approved