Simon Plouffe was one of the discoverers of the nice pi formula inf 4 2 1 1 -k pi = sum (---- - ---- - ---- - ----) 16 k=0 8k+1 8k+4 8k+5 8k+6 which allows computing individual bits of pi without computing the preceding part. It seems to me that there should be another such formula, in which the mod 8 residues are rearranged a little. Perhaps with 8k+3 and 8k+7 replacing 1 & 5, or maybe just 1&3 instead of 1&5, or with 8k+2 in place of 8k+6. Has anyone seen variations like this? ----- The sums of 1/(2n+1)^k, for even k, give rational multiples of pi^k, and the alternating sums, for odd k, also give rational multiples of pi^k. So 1 - 1/27 + 1/125 - ... = pi^3 / 32. Perhaps there's some relationship between the leftovers: gamma, Catalan, zeta(odd), etc? Rich