Let's take a (light-hearted) look at some empirical evidence. I calculated (Sum-of-Digits of 2^n)/n for a handful of random, increasingly-large n: 9*log10(2)/2 1.354634980 e/2 1.359140914 n SD(2^n)/n 48811 1.359140358 54622 1.359141005 95411 1.359140980 159152 1.359140947 506737 1.359140935 Yes of course, I'm being facetious. Back in 2006, I did this with powers of 5 and the number pi: http://oeis.org/A119666 On Apr 17, 2013, at 5:48 PM, rcs@xmission.com wrote:
Shouldn't that be 4.5 log_10(2) n? Admittedly, 1.354635 is close to 1.359141.
Quoting "W. Edwin Clark" <wclark@mail.usf.edu>:
S(n) is the sequence http://oeis.org/A001370 where it is asserted that S(n) ~ ne/2