Little Sugar (Algorithm)

I came across an interesting property about numbers . If u have a number a and you consider multiples of the number , then for some number a the sum of the digits of the multiple is divisible by the number a

More than this , if you just check till the first 4 digit number , in that base then you get to know that for all multiple of the number the above mentioned property holds.

given a sequence [1 .. N] and a base ( b) , and number a . generating the multiples is as simple as doing 1 + a , 2 + a ....

finding the sum of the digits is a given base (b) is same as finding the sum of digits for base 10 that except for base 10 , base (b) is used

in code that looks like

while(n){
sum += n % base;
n = n/base;
}

the maximum 3 digit number is a given base is
base * base * base