Taxicab$(n,2,2)$ is the smallest number expressible as the sum of 2 $n$th powers in 2 different ways. I believe only the first 4 are known:
Taxicab$(1,2,2) = 4 = 1^1 + 3^1 = 2^1 + 2^1$,
Taxicab$(2,2,2) = 50 = 1^2 + 7^2 = 5^2 + 5^2$,
Taxicab$(3,2,2) = 1729 = 1^3 + 12^3 = 9^3 + 10^3$,
Taxicab$(4,2,2)= 635318657 = 59^4 + 158^4 = 133^4 + 134^4$.
Where can I find current research on this sequence? Are there some good online resources for investigating these numbers?