Let S be a qualifying number {2,6,19,58,183...}.
Then some integer [S*10^(1/2) +/- 10^(1/2)] is the next qualifying number:
578.6968118 = 578, 1827.796488 = 1826, 5774.319007 = 5774, etc.
It's not exact but it does mean there are never more than a few numbers to check, which can be helpful once the solutions get beyond 9 or 10 digits.
Edited on September 27, 2014, 2:20 am
blackjack
flooble's webmaster puzzle