Sorry,I dont understand, why do you divinate on pc in first equation?

p1 = p0*(1+pc) + aug
p2 = p1*(1+pc) + aug = (p0*(1+pc) + aug)(1+pc) + aug = p0(1+pc)^2 + aug*((1+pc) + 1)
p3 = p2*(1+pc) + aug = (p0*(1+pc)^2 + aug*((1+pc) + 1)(1+pc) + aug =
= p0(1+pc)3 + aug((1+pc)^2 + (1+pc)) + aug = p0*(1+pc)3 + aug((1+pc)^2 + (1+pc) + 1)
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pN = p0*(1+pc)^N + aug*((1+pc)^(N-1) + (1+pc)^(N-2) + ... + (1+pc)^2 + (1+pc)^1 + (1+pc)^0)
= p0*(1+pc)^N + aug*((1+pc)^N - 1)

This solution has a mistake!
n is always overwritten to 10001.
External cycle should be do/while due to fact that even if n is a number from 1 to 100,
summ of it's digits should be counted and substracted from n.
Although I have posted correct solution, I don't know how to revove incorrect one.

actually my algorithm is little bit slower compare to yours because the run time of my algorithm is O(9*n). n is the length of the string.

Algorigthm excludes sequence begining with 0 (like "05674") because it is not 5 digit number.
Great idea!