There are no other terms < 3000. - Stefan Steinerberger, Mar 14 2006
No more terms < 50000. - David Wasserman, May 30 2008
From Jon E. Schoenfield, May 29 2010: (Start)
No more terms < 100000. It is nearly certain that no terms exist beyond 805.
Let f(n) be the sum of digits of 7^n. Let d be the number of digits, i.e., d=ceiling(log_10(7^n)).
Let s(k) be the sum of k random digits (each drawn independently from a uniform distribution over the integers 0 through 9).
As n increases, the behavior of f(n)/n becomes increasingly similar to that of s(d)/n.
The mean and variance of s(d)/n are 4.5*d/n and 28.5*d/n^2, respectively.
For large values of n, the distribution of s(d)/n approaches a standard normal distribution with mean 4.5*log_10(7) (approximately 3.80294) and variance 28.5*log_10(7)/n.
The probability P(n) that s(d)/n departs from the mean by an amount at least sufficient to reach the nearest higher or lower integer (so that n divides the sum of digits) becomes vanishingly small (e.g., P(50000) < 10^-18, P(100000) < 10^-36, P(150000) < 10^-54), and the same is true of the sum of P(i) for all i>=n (this sum is less than 10^-33 at n=100000). (End)