The (original) author checked everything up to 10^21 with a simply brute force Python program.
The more exhaustive search is referenced from The Online Encyclopedia of Integer Sequences:
Checked to 3125 (5^5) base-5 digits in just under 1/2 hour using a minor modification of the PARI program at A230360. Interestingly, with 5 replaced by 9 and the digits 2 and 3 permitted, it appears the complete set is--somewhat coincidental with this--{0, 1, 2, 3, 8281, 8282, 8283}. - James G. Merickel, Dec 01 2013
The more exhaustive search is referenced from The Online Encyclopedia of Integer Sequences:
Checked to 3125 (5^5) base-5 digits in just under 1/2 hour using a minor modification of the PARI program at A230360. Interestingly, with 5 replaced by 9 and the digits 2 and 3 permitted, it appears the complete set is--somewhat coincidental with this--{0, 1, 2, 3, 8281, 8282, 8283}. - James G. Merickel, Dec 01 2013
http://oeis.org/A146025