A161561 The smallest number larger than n with digital sum equal to n.

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 29, 39, 49, 59, 69, 79, 89, 99, 199, 299, 399, 499, 599, 699, 799, 899, 999, 1999, 2999, 3999, 4999, 5999, 6999, 7999, 8999, 9999, 19999, 29999, 39999, 49999, 59999, 69999, 79999, 89999, 99999, 199999, 299999, 399999

Offset: 1

Author

Enoch Haga, Jun 13 2009

Keywords

• base
• easy
• nonn

Examples

			a(4)=13 because the sums of digits of the candidates 5 to 12 are all different from n=4, and 13 is the first candidate with sum 1+3 = n = 4.
		

Crossrefs

Cf. A161551, A075360, A054750.

Programs

Mathematica

dsn[n_]:=Module[{k=n+1},While[Total[IntegerDigits[k]]!=n,k++];k]; Array[ dsn,50] (* Harvey P. Dale, Oct 24 2020 *)

PARI

a(n) = my(m = n+1); while(sumdigits(m) != n, m++); m; \\ Michel Marcus, Jun 08 2014

Formula

a(n) = min{k>n: A007953(k) = n}.

Extensions

More precise definition from R. J. Mathar, Aug 30 2010