[math-fun] CF inconsequentia

(Very good news, if no news is good news.) I once had a jugendtraum of showing the continued fraction of π to be aperiodic mod 2 by analyzing the process of converting one of its non-regular continued fractions to its regular one. I just looked at the simpler problem of converting 1+1/(2+2/(3+3/... to 1/(e-1). It appears that its rate of convergence is incommensurable with 2,6,10,14,. . . = coth(1/2). This should enable me to prove the geezertraum that e and e are algebraically independent. Furtherless, if x has CF = 0,1,4,9,16, ..., then (1+x)/(1-x) has quasiperiod 8, with 4 constant terms and 4 quadratics. (No linears.) —rwg