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A382068 Array read by ascending antidiagonals: A(n,m) is obtained by concatenating the digits of floor(n/m) with those of its fractional part up to the digits of the first period, where the leading and trailing 0's are omitted.

%I A382068 #13 Mar 14 2025 21:06:17
%S A382068 1,2,5,3,1,3,4,15,6,25,5,2,1,5,2,6,25,13,75,4,16,7,3,16,1,6,3,142857,
%T A382068 8,35,2,125,8,5,285714,125,9,4,23,15,1,6,428571,25,1,10,45,26,175,12,
%U A382068 83,571428,375,2,1,11,5,3,2,14,1,714285,5,3,2,9
%N A382068 Array read by ascending antidiagonals: A(n,m) is obtained by concatenating the digits of floor(n/m) with those of its fractional part up to the digits of the first period, where the leading and trailing 0's are omitted.
%e A382068 The array begins as:
%e A382068    1,  5,  3,  25,  2,  16,  142857,  125,  1,  1,  9, ...
%e A382068    2,  1,  6,   5,  4,   3,  285714,   25,  2,  2, 18, ...
%e A382068    3, 15,  1,  75,  6,   5,  428571,  375,  3,  3, 27, ...
%e A382068    4,  2, 13,   1,  8,   6,  571428,    5,  4,  4, 36, ...
%e A382068    5, 25, 16, 125,  1,  83,  714285,  625,  5,  5, 45, ...
%e A382068    6,  3,  2,  15, 12,   1,  857142,   75,  6,  6, 54, ...
%e A382068    7, 35, 23, 175, 14, 116,       1,  875,  7,  7, 63, ...
%e A382068    8,  4, 26,   2, 16,  13, 1142875,    1,  8,  8, 72, ...
%e A382068    9, 45,  3, 225, 18,  15, 1285714, 1125,  1,  9, 81, ...
%e A382068   10,  5, 33,  25,  2,  16, 1428571,  125, 11,  1, 90, ...
%e A382068   11, 55, 36, 275, 22, 183, 1571428, 1375, 12, 11,  1, ...
%e A382068   ...
%e A382068 A(4,1) = 4 since 4/1 = 4;
%e A382068 A(7,4) = 175 since 7/4 = 1.75;
%e A382068 A(5,7) = 714285 since 5/7 = 0.{714285}*, where {...}* means that these digits repeat forever.
%Y A382068 Cf. A000012 (main diagonal), A000027 (1st column), A266385 (1st row).
%K A382068 nonn,base,tabl
%O A382068 1,2
%A A382068 _Stefano Spezia_, Mar 14 2025