Minimal Niven numbers
  Define a(k,q) to be the smallest positive multiple of k such that the sum of its digits in base q is equal to k.   The asymptotic behavior, lower and upper bound estimates of a(k,q) are investigated. A characterization of the minimality condition is also considered. 
H. Fredricksen, E. J. Ionascu, F. Luca, P. Stanica