A002998 Smallest multiple of n whose digits sum to n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 190, 209, 48, 247, 266, 195, 448, 476, 198, 874, 3980, 399, 2398, 1679, 888, 4975, 1898, 999, 7588, 4988, 39990, 8959, 17888, 42999, 28798, 57995, 29988, 37999, 59888, 49998, 699880, 177899, 88998, 99889, 479996, 499995

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy
• nice

Comments

a(n) = A131382(n) * n. - Michel Marcus, Dec 10 2012

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

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

References

• Mohammed Aassila, 1000 challenges mathématiques, Algèbre, Ellipses, 2016, p. 110.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• David Wilson, Table of n, a(n) for n = 0..1000
• H. Fredricksen, E. J. Ionascu, F. Luca, and P. Stanica, Minimal Niven numbers, arXiv:0803.0477 [math.NT], 2008.
• H. Fredricksen, E. J. Ionascu, F. Luca, and P. Stanica, Minimal Niven numbers, Acta Arithmetica 132(2008), 135-159.
• H. W. Gould, Letters to N. J. A. Sloane, 1974
• David Wilson, C++ program

Crossrefs

Cf. A005349, A131382.

Programs

Mathematica

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

PARI

a(n)=my(k); while(sumdigits(k+=n)!=n,); k \\ Charles R Greathouse IV, Feb 01 2013

Extensions

More terms from Erich Friedman, Jul 04 2001