Automorphic numbers (in a specified base) have the property that the expansion of n² ends in that of n; Fairbairn characterized these numbers for all bases in 1969. Here we consider some related sequences: those n for which the sum of the first n natural numbers, squares, or cubes ends in n. For sums of natural numbers, these are Trigg's "trimorphic" numbers; for sums of squares, Pickover's "square pyramorphic" numbers. We characterize the trimorphic numbers for all bases, and the other two for base 10 and prime powers. We also solve a related problem due to Pickover.