Average digit of n^2 is s=2 (no trailing zeroes in n, please). There are 2514 such integers < 10^7: 145, 152, 179, 251, 3182, 3199, 3245, 3335, 3362,... See http://zak08.livejournal.com/14963.html Some Qs: Is there infinitude of such n's? Any general properties of such n's? Case s=1 is trivial, of course, but what about other values of s? Thanks, Zak