I think I've managed to construct a symmetric set of functions, that let's a x, x^2, x^3\; double an algebraic number.
I have a series that goes {6,9},{27,54} already. If I set x = 3, then I replace these terms with \; \{ 2x, x^2 \} ; \{ x^3, 2x^3 \}
I have the series and a symmetric set...