%I M0489 #57 Jun 30 2023 08:19:03

%S 0,1,2,3,4,5,6,7,8,9,190,209,48,247,266,195,448,476,198,874,3980,399,

%T 2398,1679,888,4975,1898,999,7588,4988,39990,8959,17888,42999,28798,

%U 57995,29988,37999,59888,49998,699880,177899,88998,99889,479996,499995

%N Smallest multiple of n whose digits sum to n.

%C a(n) = A131382(n) * n. - _Michel Marcus_, Dec 10 2012

%C The subsequence of repdigits is: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 888, 999, 999999999, 999999999999999999999999999, ... and their indices are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 24, 27, 81, 243, 729, 999, ... - _Michel Marcus_, Apr 14 2015

%C a(n) is the smallest harshad number (see A005349) whose sum of digits is n; it is not obvious that a(n) exists for all n, see Mohammed Aassila's reference. - _Robert FERREOL_, Jun 30 2023

%D Mohammed Aassila, 1000 challenges mathématiques, Algèbre, Ellipses, 2016, p. 110.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H David Wilson, <a href="/A002998/b002998.txt">Table of n, a(n) for n = 0..1000</a>

%H H. Fredricksen, E. J. Ionascu, F. Luca, and P. Stanica, <a href="http://arxiv.org/abs/0803.0477">Minimal Niven numbers</a>, arXiv:0803.0477 [math.NT], 2008.

%H H. Fredricksen, E. J. Ionascu, F. Luca, and P. Stanica, <a href="http://dx.doi.org/10.4064/aa132-2-3">Minimal Niven numbers</a>, Acta Arithmetica 132(2008), 135-159.

%H H. W. Gould, <a href="/A002998/a002998.pdf">Letters to N. J. A. Sloane, 1974</a>

%H David Wilson, <a href="/A002998/a002998.cc">C++ program</a>

%t Flatten[Table[Select[n Range[100000], Total[IntegerDigits[#]] == n&, 1], {n,0,50}]] (* _Harvey P. Dale_, Oct 30 2011 *)

%o (PARI) a(n)=my(k); while(sumdigits(k+=n)!=n,); k \\ _Charles R Greathouse IV_, Feb 01 2013

%Y Cf. A005349, A131382.

%K nonn,base,easy,nice

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Erich Friedman_, Jul 04 2001