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A159861 Square array A(m,n), m>=1, n>=1, read by antidiagonals: A(m,1)=1, A(m,n) is the rank with respect to m of the concatenation of all preceding terms in row m, and the rank of S with respect to m is floor ((S+m-1)/m).

%I A159861 #20 Feb 16 2023 16:07:34
%S A159861 1,1,1,11,1,1,1111,6,1,1,11111111,58,4,1,1,1111111111111111,5829,38,3,
%T A159861 1,1,11111111111111111111111111111111,58292915,3813,29,3,1,1,
%U A159861 1111111111111111111111111111111111111111111111111111111111111111,5829291479146458,38127938,2833,23,2,1,1
%N A159861 Square array A(m,n), m>=1, n>=1, read by antidiagonals: A(m,1)=1, A(m,n) is the rank with respect to m of the concatenation of all preceding terms in row m, and the rank of S with respect to m is floor ((S+m-1)/m).
%H A159861 Alois P. Heinz, <a href="/A159861/b159861.txt">Antidiagonals n = 1..12, flattened</a>
%e A159861 A(3,4) = 38, because A(3,1).A(3,2).A(3,3) = 114, and the rank of 114 with respect to 3 is floor(116/3) = 38.
%e A159861 Square array A(m,n) begins:
%e A159861   1,  1, 11, 1111, 11111111, 1111111111111111,  ...
%e A159861   1,  1,  6,   58,     5829,         58292915,  ...
%e A159861   1,  1,  4,   38,     3813,         38127938,  ...
%e A159861   1,  1,  3,   29,     2833,         28323209,  ...
%e A159861   1,  1,  3,   23,     2265,         22646453,  ...
%e A159861   1,  1,  2,   19,     1870,         18698645,  ...
%p A159861 R:= (S,m)-> iquo(S+m-1, m):
%p A159861 A:= proc(m, n) option remember; `if`(n=1, 1,
%p A159861       R(parse(cat(seq(A(m, j), j=1..n-1))), m))
%p A159861     end:
%p A159861 seq(seq(A(m, d-m), m=1..d-1), d=1..10);
%t A159861 R[S_, m_] := Quotient[S + m - 1, m];
%t A159861 A[m_, n_] := If[n == 1, 1, R[ToExpression@StringJoin[ToString /@ Table[A[m, j], {j, 1, n - 1}]], m]];
%t A159861 Table[Table[A[m, d - m], {m, 1, d - 1}], {d, 1, 10}] // Flatten (* _Jean-François Alcover_, Feb 13 2023, after Maple code *)
%Y A159861 Row m=2 gives: A156147.
%Y A159861 Main diagonal gives: A159862.
%Y A159861 Cf. A156146, A010783.
%K A159861 easy,nonn,tabl,base
%O A159861 1,4
%A A159861 _Eric Angelini_ and _Alois P. Heinz_, Apr 24 2009