OFFSET
2,1
COMMENTS
A digitally balanced number in base b contains every digit from 0 to b-1 in equal amount.
LINKS
Giovanni Resta, Digitally balanced numbers, Numbers Aplenty, 2013.
EXAMPLE
Array begins:
n\k| 1 2 3 4 5 ...
-------------------------------------------------------------------------
2 | 2, 9, 10, 12, 35, ... = A031443
3 | 11, 15, 19, 21, 260, ... = A049354
4 | 75, 78, 99, 108, 114, ... = A049355
5 | 694, 698, 714, 722, 738, ... = A049356
6 | 8345, 8350, 8375, 8385, 8410, ... = A049357
7 | 123717, 123723, 123759, 123771, 123807, ... = A049358
8 | 2177399, 2177406, 2177455, 2177469, 2177518, ... = A049359
9 | 44317196, 44317204, 44317268, 44317284, 44317348, ... = A049360
10 | 1023456789, 1023456798, 1023456879, 1023456897, 1023456978, ...
11 | 26432593615, 26432593625, 26432593725, 26432593745, 26432593845, ...
... | \______ A378001 (main diagonal)
T(2,4) = 12 = 1100_2 is the fourth number in base 2 containing an equal amount of zeros and ones.
T(9,5) = 44317348 = 102345867_9 is the fifth number in base 9 containing an equal amount of digits from 0 to 8.
MATHEMATICA
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]]
CROSSREFS
KEYWORD
AUTHOR
Paolo Xausa, Nov 14 2024
STATUS
approved