A087303 Smallest nontrivial multiple of n whose digit sum is the same as that of the digit sum of n. By nontrivial one means a(n) is not equal to n or (10^k)*n. 0 if no such number exists.

110, 12, 112, 140, 24, 133, 152, 18, 0, 1001, 300, 2002, 1022, 60, 304, 323, 36, 361, 1100, 10101, 1012, 11201, 312, 700, 1430, 54, 532, 551, 120, 120001, 10112, 132, 4012, 1610, 72, 703, 722, 156, 1120, 10004, 1050, 1204, 1232, 90, 1702, 1316, 192

Offset

2,1

Comments

a(10^k) does not exist, where k is any positive integer. - Pawel P. Mazur (Pawel.Mazur(AT)pwr.wroc.pl), Mar 13 2005

Dartyge, Luca, & Stanica show that a(n) = 0 iff n is a power of 10. - Charles R Greathouse IV, Oct 23 2009

Links

Table of n, a(n) for n=2..48.

Cecile Dartyge, Florian Luca and Pantelimon Stanica, On digit sums of multiples of an integer, Journal of Number Theory, 129 (2009), 2820-2830. [From Parthasarathy Nambi, Aug 22 2009]

Example

a(21) = 10101 = 481*21.

Prog

(PARI) ispow10(n)=my(k); ispower(n, , &k); k==10||n==1||n==10
a(n)=my(k, s); if(ispow10(n), 0, s=sumdigits(k=n); while(sumdigits(k+=n)!=s||ispow10(k/n), ); k) \\ Charles R Greathouse IV, Feb 04 2013

Crossrefs

Sequence in context: A282074 A282325 A266660 * A336740 A045884 A247391

Adjacent sequences: A087300 A087301 A087302 * A087304 A087305 A087306

Keyword

base,nonn

Author

Amarnath Murthy, Sep 01 2003

Extensions

More terms from Pawel P. Mazur (Pawel.Mazur(AT)pwr.wroc.pl), Mar 13 2005

Status

approved