hihi, all - one of the things i noticed is that a very large fraction (i know better than to say almost all in this group 8-)) of the values a[n] are ``late'', where late means a[n] < n the opposite ones are early, like 6 and 15 but most of the late ones are not very late, usually within a few percent of n (at least up to n=10^6, and the percentage is also decreasing, irregularly as seems to be the case with all properties related to primes) - i wonder of some kind of density argument might get somewhere it is also interesting to look at the sequence gcd(a[n],a[n-1]) for n>2, which has a subsequence that seems to be all the primes, all in order (but not consecutive; there are lotsa pesky 2's) with a density that appears to be approaching 0.5; that might be a useful step, to show that every prime p occurs in some a[n] with n < 2*p or so more soon, chris