cp's OEIS Frontend

A289281 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.

%I A289281 #11 Jul 11 2017 07:47:42
%S A289281 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 A289281 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 A289281 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 A289281 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 A289281 The generalization of A104234 (row 2) and A288577 (row 3) to arbitrary m.
%H A289281 Kerry Mitchell, <a href="/A289281/b289281.txt">Table of n, a(n) for n = 2..10012</a>
%e A289281 The array starts (first row: m=2)
%e A289281   [ 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 A289281   [ 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 A289281   [ 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 A289281   [ 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 A289281   [ 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 A289281   [ 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 A289281   [ 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 A289281   [ 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 A289281   [ 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 A289281   [ 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 A289281   [ 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 A289281   [ 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 A289281   ...
%e A289281 It is easy to prove that row m starts with (0, ..., m-1; 2, ..., m; 3, ..., m; m, ..., 2m-1; ...).
%o A289281 (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 A289281 Cf. A104234 (row 2), A288577 (row 3).
%K A289281 nonn,tabl
%O A289281 2,4
%A A289281 _M. F. Hasler_, Jul 01 2017