A159861 - OEIS

%I #20 Feb 16 2023 16:07:34

%S 1,1,1,11,1,1,1111,6,1,1,11111111,58,4,1,1,1111111111111111,5829,38,3,

%T 1,1,11111111111111111111111111111111,58292915,3813,29,3,1,1,

%U 1111111111111111111111111111111111111111111111111111111111111111,5829291479146458,38127938,2833,23,2,1,1

%N 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 Alois P. Heinz, <a href="/A159861/b159861.txt">Antidiagonals n = 1..12, flattened</a>

%e 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 Square array A(m,n) begins:

%e   1,  1, 11, 1111, 11111111, 1111111111111111,  ...

%e   1,  1,  6,   58,     5829,         58292915,  ...

%e   1,  1,  4,   38,     3813,         38127938,  ...

%e   1,  1,  3,   29,     2833,         28323209,  ...

%e   1,  1,  3,   23,     2265,         22646453,  ...

%e   1,  1,  2,   19,     1870,         18698645,  ...

%p R:= (S,m)-> iquo(S+m-1, m):

%p A:= proc(m, n) option remember; `if`(n=1, 1,

%p       R(parse(cat(seq(A(m, j), j=1..n-1))), m))

%p     end:

%p seq(seq(A(m, d-m), m=1..d-1), d=1..10);

%t R[S_, m_] := Quotient[S + m - 1, m];

%t A[m_, n_] := If[n == 1, 1, R[ToExpression@StringJoin[ToString /@ Table[A[m, j], {j, 1, n - 1}]], m]];

%t Table[Table[A[m, d - m], {m, 1, d - 1}], {d, 1, 10}] // Flatten (* _Jean-François Alcover_, Feb 13 2023, after Maple code *)

%Y Row m=2 gives: A156147.

%Y Main diagonal gives: A159862.

%Y Cf. A156146, A010783.

%K easy,nonn,tabl,base

%O 1,4

%A _Eric Angelini_ and _Alois P. Heinz_, Apr 24 2009