OFFSET
1,2
COMMENTS
a(n) <= (10^n-1)/9. a(3n) <= (10^n-1)/3.
Many, but not all of a(n) are the divisors of (10^n-1)/9.
a(17)<=5363222357, a(18)=99, a(20)=12344321, a(21)=243309, a(24)<=33333333, a(27)=999
LINKS
Author?, On sum of digits and one open problem (in Russian)
Author?, Discussion on scientific forum dxdy.ru (in Russian)
FORMULA
a(n) = smallest m such that A077196(m)=n.
a(9n) = 10^n - 1.
EXAMPLE
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.
CROSSREFS
KEYWORD
base,hard,more,nonn
AUTHOR
Alexey Izvalov, Feb 18 2010
EXTENSIONS
Edited by Max Alekseyev, Feb 19 2010, Nov 13 2010
a(21) and new bounds for a(13), a(16), a(17), a(20), a(24) from Max Alekseyev, Nov 14 2010
a(13), a(16), and a(20) from Max Alekseyev, Nov 17 2010, Nov 19 2010
STATUS
approved