Problems & Puzzles: Puzzles

Puzzle 725. The ABA numbers Here you are asked just to extend the OEIS sequence A235368 beyond the number 344373768 in order to produce the smallest ABA number with 4 distinct representations. Q. Send your next terms for this sequence.

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Contributions came from Emmanuel Vantieghem

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Emmanuel wrote:

I can say no more than that the number  (2^75)*(3^40)*(5^96)  is the smallest ABA number of the form  (2^a)(p^b)(q^c). This is a number of  109  digits.

(2^75)*(3^40)*(5^96) = 2*((2^37)*(3^20)*(5^48))^2

                                  = 8*((2^9)*(3^5)*(5^12))^8

                                  = 3*((2^25)*(3^13)*(5^32))^3

                                  =  5*((2^15)*(3^8)*(5^19))^5

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