In mathematics, a Göbel sequence is a sequence of rational numbers defined by the recurrence relation with starting value Göbel's sequence starts with The first non-integral value is x43.
[1] This sequence was developed by the German mathematician Fritz Göbel in the 1970s.
[2] In 1975, the Dutch mathematician Hendrik Lenstra showed that the 43rd term is not an integer.
[2] Göbel's sequence can be generalized to kth powers by The least indices at which the k-Göbel sequences assume a non-integral value are Regardless of the value chosen for k, the initial 19 terms are always integers.
[3][2]