PT_: I'm impressed! My own solution using ΔList(cumSum( was 44 bytes because I forgot to take the ΔList(cumSum( out of the augment(. Combining my solution and yours, we have this in 42 bytes, which seems to be optimal:
Input N
int(10fPart(.1N10^(iPart(seq(A,A,~log(N),0
While N≠max(Ans
∆List(cumSum(augment(Ans,{sum(Ans
End
N=max(Ans