%I #11 Jul 11 2017 07:47:42
%S 0,1,0,2,1,0,2,2,1,0,3,2,2,1,0,2,3,3,2,1,0,3,3,2,3,2,1,0,4,3,3,4,3,2,
%T 1,0,2,4,4,2,4,3,2,1,0,3,5,3,3,5,4,3,2,1,0,4,3,4,4,2,5,4,3,2,1,0,4,4,
%U 4,5,3,6,5,4,3,2,1,0,5,5,5,3,4,2,6,5,4,3,2,1,0,2,3,6,4,5,3,7,6,5,4,3,2,1,0,3,4,7,5,6,4,2,7,6,5,4,3,2,1,0,4,5,4,5,3,5,3,8,7,6,5,4
%N Square array whose rows m >= 2 hold the limit under iterations of the morphism { x -> (x, ..., x+k-1) if k|x ; x -> x+1 otherwise }, starting with (0); read by falling antidiagonals.
%C The generalization of A104234 (row 2) and A288577 (row 3) to arbitrary m.
%H Kerry Mitchell, <a href="/A289281/b289281.txt">Table of n, a(n) for n = 2..10012</a>
%e The array starts (first row: m=2)
%e [ 0 1 2 2 3 2 3 4 2 3 4 4 5 2 3 4 4 5 4 5 6 2 3 4 4 ...]
%e [ 0 1 2 2 3 3 3 4 5 3 4 5 3 4 5 5 6 3 4 5 5 6 3 4 5 ...]
%e [ 0 1 2 3 2 3 4 3 4 4 5 6 7 4 4 5 6 7 4 5 6 7 6 7 8 ...]
%e [ 0 1 2 3 4 2 3 4 5 3 4 5 5 6 7 8 9 4 5 5 6 7 8 9 5 ...]
%e [ 0 1 2 3 4 5 2 3 4 5 6 3 4 5 6 6 7 8 9 10 11 4 5 6 6 ...]
%e [ 0 1 2 3 4 5 6 2 3 4 5 6 7 3 4 5 6 7 7 8 9 10 11 12 13 ...]
%e [ 0 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 8 9 10 11 ...]
%e [ 0 1 2 3 4 5 6 7 8 2 3 4 5 6 7 8 9 3 4 5 6 7 8 9 9 ...]
%e [ 0 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 10 3 4 5 6 7 8 ...]
%e [ 0 1 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 11 3 4 5 6 ...]
%e [ 0 1 2 3 4 5 6 7 8 9 10 11 2 3 4 5 6 7 8 9 10 11 12 3 4 ...]
%e [ 0 1 2 3 4 5 6 7 8 9 10 11 12 2 3 4 5 6 7 8 9 10 11 12 13 ...]
%e ...
%e It is easy to prove that row m starts with (0, ..., m-1; 2, ..., m; 3, ..., m; m, ..., 2m-1; ...).
%o (PARI) A289281_row(n=30,k=2,a=[0])={while(#a<n,a=concat(vector(#a,j,if(a[j]%k,a[j]+1,vector(k,i,a[j]+i-1)))));a}
%Y Cf. A104234 (row 2), A288577 (row 3).
%K nonn,tabl
%O 2,4
%A _M. F. Hasler_, Jul 01 2017