Badulla Badu Numbers--------

( L = 2 ): ( N = S^2 ), two digits, sum digits = ( S ). Try ( S=4 ) → ( N=16 ) sum=7 no; ( S=5 ) → 25 sum=7 no; ( S=6 ) → 36 sum=9 no; ( S=7 ) → 49 sum=13 no; ( S=8 ) → 64 sum=10 no; ( S=9 ) → 81 sum=9 → (8+1=9, 9^2=81). So 81 is a Badulla Badu number.

| ( n ) | Prime factors | Base ( b ) (digit count in that base) | Palindrome in base ( b )? | |--------|----------------|-------------------------------------------|-----------------------------| | 1 | none (by convention, ( b=1 )) | 1 → “1” | Yes | | 81 | 3,3,3,3 → ( b=4 ) | 81 in base 4 = 1101 → not a palindrome | Wait, this fails — see note below | Badulla Badu Numbers--------