A061276 Numbers that are sums of repdigits of their digits (see Comments for precise definition).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 197, 198, 199, 285, 373, 461, 554, 1098, 1099, 1185, 1186, 1187, 1276, 1278, 1365, 1366, 1453, 1454, 1458, 1459, 1543, 2176, 2261, 2263, 2354, 2357, 2359, 2532, 2621, 2623, 2996, 2997, 2999, 3254, 3259, 3340, 3341, 3342, 3343

Offset

1,3

Comments

If d is 1, 2, 3, ..., or 9, let S(d) denote a decimal number of the form ddd...d, with at least one d, and let S(0) = 0.

The sequence consists of numbers k with the following property. If the decimal expansion of k is ijk..., then k can also be written as S(i)+S(j)+S(k)+...

For example, 199 is a term, because 99 = 1 + 99 + 99, which has the form S(1)+S(9)+S(9).

For further examples see the Seidov link.

Links

T. D. Noe, Table of n, a(n) for n = 1..7474 (numbers < 1000000)

Zak Seidov, Table of n, a(n) with corresponding repdigits, for n = 1..1000

Example

1185 = 1111 + 11 + 8 + 55.

Mathematica

okQ[n_] := Module[{d, len, ones, lst}, d = IntegerDigits[n]; len = Length[d]; ones = Table[(10^i - 1)/9, {i, len}]; lst = d[[1]]*ones; Do[lst = Union[Flatten[Outer[Plus, lst, d[[i]]*ones]]], {i, 2, len}]; MemberQ[lst, n]]; Select[Range[0, 4000], okQ] (* T. D. Noe, Dec 09 2011 *)

Crossrefs

Cf. A131366.

Sequence in context: A328279 A039723 A002998 * A249515 A217555 A137667

Adjacent sequences: A061273 A061274 A061275 * A061277 A061278 A061279

Keyword

base,easy,nice,nonn

Author

Erich Friedman, Jun 02 2001

Extensions

Edited by N. J. A. Sloane, Mar 19 2023

Status

approved