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

0,2

Comments

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

Links

Table of n, a(n) for n=0..77.

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.

Example

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,
  ...

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 *)

Crossrefs

Cf. A085119.

Sequence in context: A318350 A127332 A087826 * A131624 A165077 A165079

Adjacent sequences: A383457 A383458 A383459 * A383461 A383462 A383463

Keyword

nonn,tabf

Author

N. J. A. Sloane, May 30 2025

Extensions

More terms from Giorgos Kalogeropoulos, May 31 2025

Status

approved