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A329476 Main diagonal of the square array A(n,k). Let D(x) = A055642(x). Then A(1,1) = 1; A(n,n) = #{A(i,j) | D(A(i,j)) = D(A(n-1,n-1)), 1 <= i,j <= n-1}. A(i,n) = A(n,n) + n + 1 - i, 1 <= i < n (column); A(n,j) = A(1,n) + n + 1 - j, 1 <= j < n (row).

%I A329476 #33 Dec 18 2024 22:17:47
%S A329476 1,1,4,9,10,15,26,39,54,71,90,100,34,125,61,154,92,162,152,189,228,
%T A329476 269,312,357,404,453,504,557,612,669,728,789,852,917,984,1000,124,
%U A329476 1073,199,1150,278,1231,361,1316,448,1405,539,1498,634,1595,733,1696,836,1801,943
%N A329476 Main diagonal of the square array A(n,k). Let D(x) = A055642(x). Then A(1,1) = 1; A(n,n) = #{A(i,j) | D(A(i,j)) = D(A(n-1,n-1)), 1 <= i,j <= n-1}. A(i,n) = A(n,n) + n + 1 - i, 1 <= i < n (column); A(n,j) = A(1,n) + n + 1 - j, 1 <= j < n (row).
%C A329476 Main diagonal of the square array A(n,k). Define D(x) to be the number of digits of x in base 10. A(1,1) = 1; Then A(n,n) = #{A(i,j) | D(A(i,j)) = D(A(n-1,n-1)), 1 <= i,j <= n-1}. After the new diagonal A(n,n) is computed, populate the cells above and to the left of the new diagonal: A(i,n) = A(n,n) + n + 1 - i, 1 <= i < n (column); A(n,j) = A(1,n) + n + 1 - j, 1 <= j < n (row).
%e A329476 In the array below, A(5,5) = 10. Since it has two digits, we count the numbers in the array that have two digits up to that point. That would be 15. So A(6,6) = 15. Then we populate the 6th column up from the diagonal with 16, 17, 18, 19, 20. Then we populate the 6th row left from the diagonal with 21, 22, 23, 24, 25.
%e A329476    1,  2,  6, 12, 14, 20, 32, 46, 62, 80, ...
%e A329476    3,  1,  5, 11, 13, 19, 31, 45, 61, 79, ...
%e A329476    8,  7,  4, 10, 12, 18, 30, 44, 60, 78, ...
%e A329476   15, 14, 13,  9, 11, 17, 29, 43, 59, 77, ...
%e A329476   18, 17, 16, 15, 10, 16, 28, 42, 58, 76, ...
%e A329476   25, 24, 23, 22, 21, 15, 27, 41, 57, 75, ...
%e A329476   38, 37, 36, 35, 34, 33, 26, 40, 56, 74, ...
%e A329476   53, 52, 51, 50, 49, 48, 47, 39, 55, 73, ...
%e A329476   70, 69, 68, 67, 66, 65, 64, 63, 54, 72, ...
%e A329476   89, 88, 87, 86, 85, 84, 83, 82, 81, 71, ...
%Y A329476 Cf. A055642.
%K A329476 nonn,base
%O A329476 1,3
%A A329476 _Ali Sada_, Nov 13 2019