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A380390 Array read by ascending antidiagonals: A(n, k) is equal to n/k if k | n, else to the concatenation of A003988(n, k) = floor(n/k) and A380389(n - k*floor(n/k), k).

%I A380390 #12 Jan 23 2025 21:58:34
%S A380390 1,2,12,3,1,13,4,112,23,14,5,2,1,12,15,6,212,113,34,25,16,7,3,123,1,
%T A380390 35,13,17,8,312,2,114,45,12,27,18,9,4,213,112,1,23,37,14,19,10,412,
%U A380390 223,134,115,56,47,38,29,110,11,5,3,2,125,1,57,12,13,15,111
%N A380390 Array read by ascending antidiagonals: A(n, k) is equal to n/k if k | n, else to the concatenation of A003988(n, k) = floor(n/k) and A380389(n - k*floor(n/k), k).
%H A380390 Stefano Spezia, <a href="/A380390/b380390.txt">Table of n, a(n) for n = 1..11325</a> (first 150 antidiagonals of the array)
%e A380390 The array begins:
%e A380390   1,  12,  13,  14,  15,  16, 17, 18, ...
%e A380390   2,   1,  23,  12,  25,  13, 27, 14, ...
%e A380390   3, 112,   1,  34,  35,  12, 37, 38, ...
%e A380390   4,   2, 113,   1,  45,  23, 47, 12, ...
%e A380390   5, 212, 123, 114,   1,  56, 57, 58, ...
%e A380390   6,   3,   2, 112, 115,   1, 67, 34, ...
%e A380390   7, 312, 213, 134, 125, 116,  1, 78, ...
%e A380390   ...
%e A380390 A(3, 2) = 112 since 3/2 = 1 + 1/2.
%e A380390 A(4, 2) = 2 since 4/2 = 2.
%t A380390 A[n_, k_]:=If[Divisible[n, k], n/k, FromDigits[Join[IntegerDigits[q=Floor[n/k]], IntegerDigits[Numerator[r=n/k-q]],IntegerDigits[Denominator[r]]]]]; Table[A[n-k+1, k], {n, 12}, {k, n}]//Flatten
%Y A380390 Cf. A003988, A372523, A380389.
%Y A380390 Cf. A000012 (diagonal), A000027 (1st column).
%K A380390 nonn,base,easy,look,tabl
%O A380390 1,2
%A A380390 _Stefano Spezia_, Jan 23 2025