A110081... begins 1, 7, 25, 31... But that doesn't agree with my results. ... please name a real number which can't be represented by {0, 1, -4}. Or by {0, 1, -10}.

By Matula's lemma 3, {0,1,-4} doesn't represent 2. (More generally, {0,1,-(6n+4)} doesn't represent (3n+2).) The proof is straightforward (and correct, I hope): With {0,1,-4} digits, base 3: if the digit sequence (d_1 d_2 d_3 ... d_n) represents 2, then d_n must be -4, and so (d_1 d_2 d_3 ... d_{n-1}) represents [2 - (-4)] / 3 = 2. Inducing, there must be a single digit that represents 2. But there isn't. That treats only integer-like finite representations. But I doubt there's an infinite representation for 2. (1.??????...?)

I've confirmed that all integers up to at least 300 can be represented with a 7-digit ternary number using those digits.

!? Please show how {0,1,-4} makes 2. -- Don Reble djr@nk.ca