Using mere long doubles in C, here are the fracfac coefficients that I believe, for 1/p, p prime <= 19. Apparently, we always have: a) (p-1)/2 is the coefficient of 1/(p-2)! (for p > 3), b) 0 is the coefficient of 1/(p-1)!, and c) p-1 is the coefficient of 1/p!. Can someone give a nice proof of these apparent patterns? --Dan coefficient of 1/factorial of 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ------------------------------------------------------------------------------------------------------------- prime p ------- 2: 1 3: 0 2 5 0 1 0 3 7: 0 0 3 2 0 6 11: 0 0 2 0 5 3 1 4 0 10 13: 0 0 1 4 1 2 5 4 8 5 0 12 17: 0 0 1 2 0 2 3 6 8 9 0 9 2 7 0 16 19: 0 0 1 1 1 6 2 0 9 5 2 6 11 11 13 8 0 18 ------------------------------------------------------------------------------------------------------------- coefficient of 1/factorial of 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 I wrote: << . . . [E]very x in (0,1) has a unique representation of the form x = Sum_{n=1..oo} c_n/(n+1)! if the integers c_n satisfy 0 <= c_n <= n. . . .
________________________________________________________________________________________ It goes without saying that .