This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A378000 #20 Nov 17 2024 07:23:53
%S A378000 2,11,9,75,15,10,694,78,19,12,8345,698,99,21,35,123717,8350,714,108,
%T A378000 260,37,2177399,123723,8375,722,114,266,38,44317196,2177406,123759,
%U A378000 8385,738,120,268,41,1023456789,44317204,2177455,123771,8410,742,135,278,42
%N A378000 Array read by ascending antidiagonals: T(n,k) is the k-th positive integer that is digitally balanced in base n.
%C A378000 A digitally balanced number in base b contains every digit from 0 to b-1 in equal amount.
%H A378000 Giovanni Resta, <a href="https://www.numbersaplenty.com/set/balanced_number/">Digitally balanced numbers</a>, Numbers Aplenty, 2013.
%e A378000 Array begins:
%e A378000 n\k| 1 2 3 4 5 ...
%e A378000 -------------------------------------------------------------------------
%e A378000 2 | 2, 9, 10, 12, 35, ... = A031443
%e A378000 3 | 11, 15, 19, 21, 260, ... = A049354
%e A378000 4 | 75, 78, 99, 108, 114, ... = A049355
%e A378000 5 | 694, 698, 714, 722, 738, ... = A049356
%e A378000 6 | 8345, 8350, 8375, 8385, 8410, ... = A049357
%e A378000 7 | 123717, 123723, 123759, 123771, 123807, ... = A049358
%e A378000 8 | 2177399, 2177406, 2177455, 2177469, 2177518, ... = A049359
%e A378000 9 | 44317196, 44317204, 44317268, 44317284, 44317348, ... = A049360
%e A378000 10 | 1023456789, 1023456798, 1023456879, 1023456897, 1023456978, ...
%e A378000 11 | 26432593615, 26432593625, 26432593725, 26432593745, 26432593845, ...
%e A378000 ... | \______ A378001 (main diagonal)
%e A378000 A049363
%e A378000 T(2,4) = 12 = 1100_2 is the fourth number in base 2 containing an equal amount of zeros and ones.
%e A378000 T(9,5) = 44317348 = 102345867_9 is the fifth number in base 9 containing an equal amount of digits from 0 to 8.
%t A378000 Module[{dmax = 10, a, m}, a = Table[m = FromDigits[Join[{1, 0}, Range[2, n-1]], n] - 1; Table[While[!SameQ@@DigitCount[++m, n]]; m, dmax-n+2], {n, dmax+1, 2, -1}]; Array[Diagonal[a, # - dmax] &, dmax]]
%Y A378000 Cf. rows 2..9: A031443, A049354, A049355, A049356, A049357, A049358, A049359, A049360.
%Y A378000 Cf. A049363 (first column, from n = 2), A378001 (main diagonal).
%Y A378000 Cf. A049364, A065963, A378073, A378080, A378104.
%K A378000 nonn,base,tabl
%O A378000 2,1
%A A378000 _Paolo Xausa_, Nov 14 2024