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%I #20 Sep 22 2013 23:07:00
%S 1,7,3,79,41,33,239,2629,9,2981,21649,813,3000811,51139,13947,5165039
%N Minimal positive integer such that the smallest possible sum of digits of its multiple equals n.
%C a(n) <= (10^n-1)/9. a(3n) <= (10^n-1)/3.
%C Many, but not all of a(n) are the divisors of (10^n-1)/9.
%C a(17)<=5363222357, a(18)=99, a(20)=12344321, a(21)=243309, a(24)<=33333333, a(27)=999
%H Author?, <a href="http://www.intelmath.narod.ru/article_minmds.html">On sum of digits and one open problem</a> (in Russian)
%H Author?, <a href="http://dxdy.ru/topic20061.html">Discussion on scientific forum dxdy.ru</a> (in Russian)
%F a(n) = smallest m such that A077196(m)=n.
%F a(9n) = 10^n - 1.
%e a(4)=79 because the sum of digits of 79*1519=120001 is 4; there is no multiple of 79 whose sum of digits is less than 4; and there is no integer smaller than 79, for which the minimal sum of digits in its multiple is 4.
%Y Cf. A077194, A077195, A077196.
%K base,hard,more,nonn
%O 1,2
%A _Alexey Izvalov_, Feb 18 2010
%E Edited by _Max Alekseyev_, Feb 19 2010, Nov 13 2010
%E a(21) and new bounds for a(13), a(16), a(17), a(20), a(24) from _Max Alekseyev_, Nov 14 2010
%E a(13), a(16), and a(20) from _Max Alekseyev_, Nov 17 2010, Nov 19 2010
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