Perfect Power Sequence
February 16, 2018
I discovered the Numberphile channel on YouTube a few months ago, and have greatly enjoyed its videos at the intersection of mathematics and programming. Their recent video discusses the Catalan Conjecture:
In the infinite sequence of perfect powers 1, 4, 8, 9, 16, 25, 32, 36, 49, 64, 81, 100, …, the only two adjacent numbers are 2³ = 8 and 3² = 9.
The conjecture has recently been proved, as discussed at Numberphile.
Your task is to write a program that generates the perfect power sequence. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.
Programming Praxis 