OFFSET
1,3
COMMENTS
Sequence is trivially infinite.
If we regard m-digit repdigits that repeat digit k as rows of a number triangle T(m, k) and we ignore the term 0, then we would have k = (1, ..., 9) for m = 1 (mod 9), k = (3, 6, 9) for m = 4 or 7 (mod 9), and k = 9 for all other values of m (mod 9). Thus the row lengths L for increasing values of m starting with m = 1 are {9, 1, 1, 3, 1, 1, 3, 1, 1} repeated. - Michael De Vlieger, Jul 13 2016.
EXAMPLE
3333 is a term because 3 + 3 + 3 + 3 = 12, 1 + 2 = 3.
MATHEMATICA
Union@ Flatten@ Table[Map[Function[k, If[NestWhile[Total@ IntegerDigits@ # &, #, IntegerLength@ # > 1 &] == k, #, 0] &@ FromDigits@ Table[k, {n}]], Range@ 9], {n, 13}] (* Michael De Vlieger, Jul 13 2016 *)
CROSSREFS
KEYWORD
nonn,easy,base,less
AUTHOR
Altug Alkan, Jul 13 2016
STATUS
approved