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A385623 Array read by ascending antidiagonals: A(n,k) is the number obtained by concatenation of n with k in that order, with k >= 0.

%I A385623 #17 Jul 11 2025 15:37:30
%S A385623 0,10,1,20,11,2,30,21,12,3,40,31,22,13,4,50,41,32,23,14,5,60,51,42,33,
%T A385623 24,15,6,70,61,52,43,34,25,16,7,80,71,62,53,44,35,26,17,8,90,81,72,63,
%U A385623 54,45,36,27,18,9,100,91,82,73,64,55,46,37,28,19,10,110,101,92,83,74,65,56,47,38,29,110,11
%N A385623 Array read by ascending antidiagonals: A(n,k) is the number obtained by concatenation of n with k in that order, with k >= 0.
%H A385623 Stefano Spezia, <a href="/A385623/b385623.txt">Table of n, a(n) for n = 0..11475</a> (first 151 antidiagonals of the array, flattened)
%F A385623 A(n,0) = 10*n and A(n,k) = n*10^(floor(log_10(k)) + 1) + k for k > 0.
%e A385623 Array begins as:
%e A385623    0,  1,  2,  3,  4,  5,  6,  7, ...
%e A385623   10, 11, 12, 13, 14, 15, 16, 17, ...
%e A385623   20, 21, 22, 23, 24, 25, 26, 27, ...
%e A385623   30, 31, 32, 33, 34, 35, 36, 37, ...
%e A385623   40, 41, 42, 43, 44, 45, 46, 47, ...
%e A385623   50, 51, 52, 53, 54, 55, 56, 57, ...
%e A385623   60, 61, 62, 63, 64, 65, 66, 67, ...
%e A385623   ...
%t A385623 A[n_,k_]:=FromDigits[Join[IntegerDigits[n],IntegerDigits[k]]]; Table[A[n,k],{n,0,6},{k,0,7}] (* or *)
%t A385623 A[n_,k_]:=If[k==0,10n,n*10^(Floor[Log10[k]]+1)+k]; Table[A[n-k,k],{n,0,11},{k,0,n}]//Flatten
%o A385623 (PARI) T(n, k) = fromdigits(concat(digits(n), digits(k))); \\ _Michel Marcus_, Jul 06 2025
%Y A385623 Columns for k=0..9 give: A008592, A017281, A017293, A017305, A017317, A017329, A017341, A017353, A017365, A017377.
%Y A385623 Cf. A001477 (1st row), A020338 (main diagonal), A055642, A385624 (antidiagonal sums).
%K A385623 nonn,base,easy,look,tabl
%O A385623 0,2
%A A385623 _Stefano Spezia_, Jul 05 2025