If the upper limit is changed to include 10^n, the entries are increased by 1 for n = 3, 4, 5,.. and perhaps others, because 1000, 10000 and 100000 are not sums of consecutive primes, whereas 10=2+3+5 and 100=2+3+5+...+19+23 are. -
R. J. Mathar, Oct 10 2010
Based on work of Enoch Haga, Jud McCranie and Felice Russo.
The ratio a(n)/10^n might be converging to 0.52..., it might also be slowly growing to 1, which way is it? -
Daniel Forgues, Nov 03 2011
