For example, 648 is the first ABA number with two representations, and .
According to Robert Munafo, the smallest number with 3 such representations is 344373768, which is equal to , and .
It is not difficult to build larger examples of numbers with 3 representations, but they actually tend to be quite larger. For example,
or or, for an odd example,In general, it is possible to construct a number with an arbitrary number of representations, of the form
where the are the prime numbers 2, 3, 5,.... and clearly . Expressing as , it is possible to find the exponents 's, and thus , by solving the system of modular equations where is the product of the primes from to and ranges from to .For example, a number of 255 digits with 4 such representations is and one of 2549 digits with 5 representations is .
The smallest Pythagorean triples made of ABA numbers are (98304, 131072, 163840) and (229376, 786432, 819200) which correspond to and .
The first ABA numbers are 8, 18, 24, 32, 50, 64, 72, 81, 98, 128, 160, 162, 192, 200 more terms