  Following Stolarsky, we say that a natural number n is flimsy in base b if
some positive multiple of n has smaller digit sum in base b than n does;
otherwise it is sturdy. We develop algorithmic methods for the study of sturdy
and flimsy numbers.
  We provide some criteria for determining whether a number is sturdy. Focusing
on the case of base b = 2, we study the computational problem of checking
whether a given number is sturdy, giving several algorithms for the problem. We
find two additional, previously unknown sturdy primes. We develop a method for
determining which numbers with a fixed number of 0's in binary are flimsy.
Finally, we develop a method that allows us to estimate the number of k-flimsy
numbers with n bits, and we provide explicit results for k = 3 and k = 5. Our
results demonstrate the utility (and fun) of creating algorithms for number
theory problems, based on methods of automata theory.
