3 ms·

How many powers of 2 have just a single even digit? 2, 4, 8, 16, 32, 512...

• madcaptenor 2y ago
  Looks like that's all of them. The typical number of even digits of n grows like a constant times n, so you need some very large deviations from t I'd conjecture the number of powers of 2 with exactly m even digits is finite for all m.
  • esnard 2y ago
    Just tested up to 2 * 1000000, and it indeed looks like that's all of them.
    • recursive 2y ago
      Asterisk means exponent here?
      • esnard 2y ago
        Yes. I didn't escape the asterisks before posting, and HN replaced ** with \* without me noticing.
• sltkr 2y ago
  This is equivalent to asking: how many powers of 2 are there such that all digits except the leading digit are 5 or greater? The powers of 2 with a single even digit are just those double those numbers (i.e., the next higher power of 2).