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

%I A383460 #15 Jun 05 2025 00:31:32
%S A383460 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,
%T A383460 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,
%U A383460 9,9,9,9,9,9,5,1,4,8,12,12
%N A383460 13 X oo array read by antidiagonals, giving the values of the standard mod 13 Ackermann function.
%C A383460 The sixth and later columns consist of all 9's, and so the antidiagonals beyond that point also consist of all 9's.
%H A383460 J. Froemke and J. W. Grossman, <a href="http://www.jstor.org/stable/2323780">A mod-n Ackermann function, or what's so special about 1969?</a>, Amer. Math. Monthly, 100 (1993), 180-183. See Fig. 1.
%e A383460 The first few antidiagonals are:
%e A383460   1,
%e A383460   2, 2,
%e A383460   3, 3, 3,
%e A383460   5, 5, 4, 4,
%e A383460   0, 0, 7, 5, 5,
%e A383460   5, 5, 3, 9, 6, 6,
%e A383460   9, 9, 6, 9, 11, 7, 7,
%e A383460   9, 9, 5, 2, 8, 0, 8, 8,
%e A383460   9, 9, 9, 9, 3, 6, 2, 9, 9,
%e A383460   ...
%t A383460 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 *)
%Y A383460 Cf. A085119.
%K A383460 nonn,tabf
%O A383460 0,2
%A A383460 _N. J. A. Sloane_, May 30 2025
%E A383460 More terms from _Giorgos Kalogeropoulos_, May 31 2025