Re: [math-fun] Exactly Distributed Digits in the Initial Digits of Pi

I have been informed by Warren D. Smith that it is known that 1- and 2-dimensional random walks are recurrent, while 3-dimensional (and higher) such walks are transient. From that perspective, it strikes me that the sequence 15, 18, ... (third term > 8*10^9) [the number of initial digits of ternary pi where the digits 0, 1, and 2 appear exactly the same number of times] should be recurrent because it can be modeled by a 2-dimensional (presumably random) walk (just as I had done in my blog article). The implication would be that this sequence is infinite!