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%I #12 Aug 27 2015 02:38:40
%S 110,12,112,140,24,133,152,18,0,1001,300,2002,1022,60,304,323,36,361,
%T 1100,10101,1012,11201,312,700,1430,54,532,551,120,120001,10112,132,
%U 4012,1610,72,703,722,156,1120,10004,1050,1204,1232,90,1702,1316,192
%N 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.
%C a(10^k) does not exist, where k is any positive integer. - Pawel P. Mazur (Pawel.Mazur(AT)pwr.wroc.pl), Mar 13 2005
%C Dartyge, Luca, & Stanica show that a(n) = 0 iff n is a power of 10. - _Charles R Greathouse IV_, Oct 23 2009
%H Cecile Dartyge, Florian Luca and Pantelimon Stanica, <a href="http://dx.doi.org/10.1016/j.jnt.2009.04.003">On digit sums of multiples of an integer</a>, Journal of Number Theory, 129 (2009), 2820-2830. [From _Parthasarathy Nambi_, Aug 22 2009]
%e a(21) = 10101 = 481*21.
%o (PARI) ispow10(n)=my(k);ispower(n,,&k); k==10||n==1||n==10
%o 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
%K base,nonn
%O 2,1
%A _Amarnath Murthy_, Sep 01 2003
%E More terms from Pawel P. Mazur (Pawel.Mazur(AT)pwr.wroc.pl), Mar 13 2005
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