3 ms·

The approximate linearity is amazing!

• JoachimSchipper 15y ago
  For a random number m, you'd expect about 1/10 digits to be zero. Why is it surprising that 2^n would behave somewhat similarly?
  • baq 15y ago
    you'd have to prove that 2^n has a uniform distribution of digits in base 10.
  • qntm 15y ago
    The numbers 2^n aren't random. For example, the final digit is never 0. You might expect other patterns to appear on larger scales.
• cft 15y ago
  The fact that it's linear actually hints that the distribution of digits is actually random: the probability of 0 in any position other than the first and the last is indeed approaching 1/10, as n goes to infinity.