Badulla Badu Numbers-------- < PRO · STRATEGY >

We need ( N = S^L ), ( N ) has ( L ) decimal digits, sum of digits = ( S ).

Check small ( L ):

Known base-10 Badulla Badu numbers (nontrivial, ( L \ge 2 )):
81, 512, 2401
Check 81 (2 digits), 512 (3 digits), 2401 (4 digits).
Next? Possibly none for higher ( L ) due to growth constraints. Badulla Badu Numbers--------

According to scattered online references (circa 2015–2023), the process for finding the Badulla Badu Numbers associated with any integer is as follows:

The repeating cycle is the Badulla Badu Pair. The numbers within that pair — typically small integers like (2, 3) or (4, 5) — are the "Badulla Badu Numbers" for that starting point. We need ( N = S^L ), (

If you wish to search for your own Badulla Badu Numbers, follow this algorithm:

Using this, the first few candidates above 100? Let’s test 102: Known base-10 Badulla Badu numbers (nontrivial, ( L

Thus, only 12 works among small numbers. Perhaps the sequence is finite and trivial—but that itself would be an interesting result.