[nngxlbde] cube root of 2

we propose 2^(1/3) ~= 1.2599210498948731647672106072782284 (previously) to be the simplest number that looks random in any base and also in its simple continued fraction.

define the simpleness of a number as the ease of computing it to arbitrary precision in any base.  for cbrt(2), Newton's method suffices.  in contrast, high precision calculation of pi is a more complicated affair.  I think it will be easy to exceed record pi calculations with those of cube root of 2.

previously, on the ease of computing the square root of 0.5, which has a periodic simple continued fraction.

the cube root of two does have a general continued fraction with a non-random looking form, as does pi.  what is the simplest number which has no non-random looking general continued fraction?  if a number looks non-random in some base, e.g., Liouville's constant, can it always be converted into a non-random looking general continued fraction?  many numbers with compact infinite series can be converted into non-random looking general continued fractions.

another candidate avoiding a non-random looking simple continued fraction: sqrt(2)+sqrt(3) ~= 3.1462643699419723423291350657155704 .  however, this feels like a cheating way of avoiding a periodic simple continued fraction, and there is no longer an easy formula to check the result.

3^(1/3) ~= 1.442249570307408382 has a nice symmetry to it.  10^(1/3) ~= 2.15443469 seems appropriate for calculating its digits or continued fraction in base 10.