Conjecturally, the last element of A020495 (a(21) = 21679) is the largest number which is neither a square nor square + prime. Likewise, the last element of A045911 (a(6195) = 78526384) is the conjectured largest number which is neither a (positive) cube or a cube + prime. In each case, the sequence is statistically finite, and a large range has been searched for additional elements, so there is a reasonable argument that these sequences are finite and correct. This, of course, suggests a sequence starting 21697, 78526384, ... The next element would the largest value which is neither a fourth power nor a fourth power + prime. This number will be very large. Looks like a real programming challenge.