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Numbers that are sums of repdigits of their digits (see Comments for precise definition).
2

%I #37 Mar 19 2023 14:13:33

%S 0,1,2,3,4,5,6,7,8,9,197,198,199,285,373,461,554,1098,1099,1185,1186,

%T 1187,1276,1278,1365,1366,1453,1454,1458,1459,1543,2176,2261,2263,

%U 2354,2357,2359,2532,2621,2623,2996,2997,2999,3254,3259,3340,3341,3342,3343

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

%C 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.

%C 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)+...

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

%C For further examples see the Seidov link.

%H T. D. Noe, <a href="/A061276/b061276.txt">Table of n, a(n) for n = 1..7474</a> (numbers < 1000000)

%H Zak Seidov, <a href="/A061276/a061276.txt">Table of n, a(n) with corresponding repdigits, for n = 1..1000</a>

%e 1185 = 1111 + 11 + 8 + 55.

%t 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 *)

%Y Cf. A131366.

%K base,easy,nice,nonn

%O 1,3

%A _Erich Friedman_, Jun 02 2001

%E Edited by _N. J. A. Sloane_, Mar 19 2023