Hello, no, I don't think it does work, pi in factorial base, that is the whole point. I tried that for years, getting the n'th digit of e or Pi in factorial base, I was convinced that I could do the n'th decimal digit of e. There is a paper of Sierpinski about factorial bases, somewhere in his collected work, see vol 1. Many of the ideas in that paper where used later to make a general base algorithm. I have one with over 500 variants of that. The thing with these bases and representations is one of the reasons why I joined Neil Sloane in the adventure of the EIS, OEIS, and HIS to get the answer about that. Well, there are no definite answer. In the factorial base , the number E is 1, of course but Pi is messy and completely random. If you use Pi and one of the Newton, Gregory or any natural bases for that number , that's ok but then E is no longer natural. If you use general continued fractions, for E, Pi and sqrt(2) , well that's better BUT there is gamma which has no representation and we go back to square one. There is no universal answer to this question so far. So far, the real numbers if represented in base 2 for example, is just a huge grey wall with no patterns whatsoever. There is a simple way to get the factorial coeffs. from a number using a greedy algorithm. here is a maple version of this : r2fact:=proc(s) local max, liste, prod, S, T, k; S := evalf(frac(abs(s))); max := 10^(Digits - 2); prod := 1; k := 1; liste := [trunc(s)]; while prod <= max do T := trunc(k!*S); S := S - T/k!; liste := [op(liste), T]; k := k + 1; prod := prod*k end do; RETURN(liste) end proc when used on Pi : 3, 0, 0, 0, 3, 1, 5, 6, 5, 0, 1, 4, 7, 8, 0, 6, 7, 10, 7, 10, 4, 10, 6, 16, 1, 11, 20, 3, 18, 12, 9, 13, 18, 21, 14, 34, 27, 11, 27, 33, ... can you see any pattern in this ?? not me. not gfun either. this is the puzzle number 7514, or if you want : A007514. Best regards, Simon Plouffe