Given an increasing sequence of positive integers a_1 < a_2 < a_3 < ... we can look at their residues mod p for p prime. In order to compare the results, we might want to think of these p-residues as divided by p and viewed in the unit interval [0,1). Someone did just that for the sequence f_n := Sum_{1<=k<=n} k! and the resulting sequence of fractions x_n := {(Sum_{1<=k<=n} k! mod p) / p as he displayed it in [0,1) varied surprisingly little across primes. * * * ALSO: This same increasing sequence f_n of integers seems to have an interestingly limited set of prime factors 3, 11, 17, 73, 97, 141, 347, 467,... (not necessarily excluding smaller ones). Also, Wolfram ( http://mathworld.wolfram.com/FactorialSums.html ) states that the sequence fsq_n := f_n := Sum_{1<=k<=n} (k!)^2 contains only a finite set of primes among its terms. Amazing! Is there some easy way to see this? --Dan