A383460 13 X oo array read by antidiagonals, giving the values of the standard mod 13 Ackermann function.

1, 2, 2, 3, 3, 3, 5, 5, 4, 4, 0, 0, 7, 5, 5, 5, 5, 3, 9, 6, 6, 9, 9, 6, 9, 11, 7, 7, 9, 9, 5, 2, 8, 0, 8, 8, 9, 9, 9, 9, 3, 6, 2, 9, 9, 9, 9, 9, 9, 5, 9, 2, 4, 10, 10, 9, 9, 9, 9, 9, 9, 11, 7, 6, 11, 11, 9, 9, 9, 9, 9, 9, 5, 1, 4, 8, 12, 12

Offset: 0

Author

N. J. A. Sloane, May 30 2025

Keywords

• nonn
• tabf

Comments

The sixth and later columns consist of all 9's, and so the antidiagonals beyond that point also consist of all 9's.

Examples

			The first few antidiagonals are:
  1,
  2, 2,
  3, 3, 3,
  5, 5, 4, 4,
  0, 0, 7, 5, 5,
  5, 5, 3, 9, 6, 6,
  9, 9, 6, 9, 11, 7, 7,
  9, 9, 5, 2, 8, 0, 8, 8,
  9, 9, 9, 9, 3, 6, 2, 9, 9,
  ...
		

Links

• J. Froemke and J. W. Grossman, A mod-n Ackermann function, or what's so special about 1969?, Amer. Math. Monthly, 100 (1993), 180-183. See Fig. 1.

Crossrefs

Cf. A085119.

Programs

Mathematica

n=12;a[i_,j_]:=a[i,j]=If[i==0,Mod[j+1,13],If[j==0,a[i-1,1],a[i-1,a[i,j-1]]]]; Flatten@Table[Diagonal[Reverse@Table[a[i,j],{i,0,n},{j,0,n}],k-n-1],{k,n}] (* Giorgos Kalogeropoulos, May 31 2025 *)

Extensions

More terms from Giorgos Kalogeropoulos, May 31 2025