Working on isometric paths in hypercubes, I came up with the following simple, yet (imo) interesting problem. For what natural numbers $n$ exists a natural number $t$ such that $n^2+n+2=2^t$? The first few terms are $n=0,1,2,5,90$, and these are all below one million. Does someone have any idea how to approach this problem? I basically only want to know whether there exist infinitely many $n$ or not (maybe even that 0, 1, 2, 5, and 90 are the only possible ones).