Re: [math-fun] Re: Number of ones in the binary expansion of 3^n

Don Reble wrote:

More likely, a(n)/n should tend to log_2(3)/2 = 0.79248+, since a bit is equally likely to be 0 or 1. (Well, the first and last bits are ones; I meant the other bits.)

The fours bit is always zero. Other bits (at least up to the 2^29s position) are exactly balanced. Dan