In mathematics, a Göbel sequence is a sequence of rational numbers defined by the recurrence relation

with starting value

Göbel's sequence starts with 1, 1, 2, 3, 5, 10, 28, 154, 3520, 1551880, ... The first non-integral value is x44.

History This sequence was developed by the German mathematician Fritz Göbel in the 1970s. In 1975, the Dutch mathematician Hendrik Lenstra showed that the 44th term is not an integer.

Generalization Göbel's sequence can be generalized to kth powers by

with starting value

The least indices at which the k-Göbel sequences assume a non-integral value are 43, 89, 97, 214, 19, 239, 37, 79, 83, 239, ... Regardless of the value chosen for k, the initial 19 terms are always integers.

See also

Somos sequence

References

External links Göbel's Sequence