Output the simplified Goodstein sequence
Python 2, 77 74 bytes

-3 bytes thanks to Lynn

n=input();b=1
while n:print"+".join(n/b*[`b`]+[`n%b`][:n%b]);n+=n/b-1;b+=1


Try it online!

Easily runs up to n = 100 (though the output is too long for tio fully show).