A271569 Repdigit numbers n such that the repeated digit of n is equal to the digital root of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 99, 999, 3333, 6666, 9999, 99999, 999999, 3333333, 6666666, 9999999, 99999999, 999999999, 1111111111, 2222222222, 3333333333, 4444444444, 5555555555, 6666666666, 7777777777, 8888888888, 9999999999, 99999999999, 999999999999, 3333333333333, 6666666666666, 9999999999999

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.

Links

Table of n, a(n) for n=1..36.

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

Cf. A010785, A010888.

Sequence in context: A378835 A281091 A378837 * A239138 A345964 A298425

Adjacent sequences: A271566 A271567 A271568 * A271570 A271571 A271572

Keyword

nonn,easy,base,less

Author

Altug Alkan, Jul 13 2016

Status

approved