Least number not representable as the sum of n repdigit numbers.
10, 21, 320, 2219, 32218, 332217, 3332216
1
It appears that the n-th term is less than or equal to 10^n. So 3332216 is not representable as the sum of 7 repdigit numbers, but the number before it is: 3332215 = 2222222 + 999999 + 99999 + 8888 + 999 + 99 + 9. The n-th number appears to be converging to 10^n/3. See S000926 for the least number of repdigit numbers that sum to a given number.
T. D. Noe, Plot of 7 terms
Eric W. Weisstein, MathWorld: Repdigit
(Mma) maxLen = 6; repNums = Union[Flatten[Table[FromDigits[Table[a, {len}]], {a, 0, 9}, {len, maxLen}]]]; last = repNums; t = {Complement[Range[last[[-1]]], last][[1]]}; Do[last = Union[Flatten[Outer[Plus, repNums, last]]]; AppendTo[t, Complement[Range[last[[-1]]], last][[1]]], {i, 2, maxLen}]; t
nonn,base,hard
T. D. Noe, Jul 26 2016