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A380389 Array read by ascending antidiagonals: A(n, k) is equal to n/k if k | n, else to the concatenation of the numerator and the denominator of n/k.

%I A380389 #10 Jan 23 2025 21:58:27
%S A380389 1,2,12,3,1,13,4,32,23,14,5,2,1,12,15,6,52,43,34,25,16,7,3,53,1,35,13,
%T A380389 17,8,72,2,54,45,12,27,18,9,4,73,32,1,23,37,14,19,10,92,83,74,65,56,
%U A380389 47,38,29,110,11,5,3,2,75,1,57,12,13,15,111,12,112,103,94,85,76,67,58,49,310,211,112
%N A380389 Array read by ascending antidiagonals: A(n, k) is equal to n/k if k | n, else to the concatenation of the numerator and the denominator of n/k.
%H A380389 Stefano Spezia, <a href="/A380389/b380389.txt">Table of n, a(n) for n = 1..11325</a> (first 150 antidiagonals of the array)
%e A380389 The array begins as:
%e A380389   1, 12, 13, 14, 15, 16, 17, 18, ...
%e A380389   2,  1, 23, 12, 25, 13, 27, 14, ...
%e A380389   3, 32,  1, 34, 35, 12, 37, 38, ...
%e A380389   4,  2, 43,  1, 45, 23, 47, 12, ...
%e A380389   5, 52, 53, 54,  1, 56, 57, 58, ...
%e A380389   6,  3,  2, 32, 65,  1, 67, 34, ...
%e A380389   7, 72, 73, 74, 75, 76,  1, 78, ...
%e A380389   ...
%e A380389 A(6, 4) = 32 since 6/4 = 3/2.
%e A380389 A(6, 3) = 2 since 6/3 = 2.
%t A380389 A[n_, k_]:=If[Divisible[n, k], n/k, FromDigits[Join[IntegerDigits[Numerator[n/k]], IntegerDigits[Denominator[n/k]]]]]; Table[A[n-k+1, k], {n, 12}, {k, n}]//Flatten
%Y A380389 Cf. A003988, A372523, A380390.
%Y A380389 Cf. A000012 (diagonal), A000027 (1st column).
%K A380389 nonn,base,easy,look,tabl
%O A380389 1,2
%A A380389 _Stefano Spezia_, Jan 23 2025