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A378000
Array read by ascending antidiagonals: T(n,k) is the k-th positive integer that is digitally balanced in base n.
14
2, 11, 9, 75, 15, 10, 694, 78, 19, 12, 8345, 698, 99, 21, 35, 123717, 8350, 714, 108, 260, 37, 2177399, 123723, 8375, 722, 114, 266, 38, 44317196, 2177406, 123759, 8385, 738, 120, 268, 41, 1023456789, 44317204, 2177455, 123771, 8410, 742, 135, 278, 42
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
Cf. A049363 (first column, from n = 2), A378001 (main diagonal).
Sequence in context: A009204 A023642 A025536 * A162155 A163344 A064743
KEYWORD
nonn,base,tabl
AUTHOR
Paolo Xausa, Nov 14 2024
STATUS
approved