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A271569 Repdigit numbers n such that the repeated digit of n is equal to the digital root of n. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A071271 A066492 A281091 * A239138 A298425 A001633

Adjacent sequences:  A271566 A271567 A271568 * A271570 A271571 A271572

KEYWORD

nonn,easy,base,less

AUTHOR

Altug Alkan, Jul 13 2016

STATUS

approved

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Last modified February 21 02:19 EST 2018. Contains 299388 sequences. (Running on oeis4.)