Editing Periodic sequence (section)

==Definition==
A '''(purely) periodic''' sequence (with '''period ''p'''''), or a '''''p-''periodic sequence''', is a sequence ''a''<sub>1</sub>, ''a''<sub>2</sub>, ''a''<sub>3</sub>, ... satisfying

:''a''<sub>''n''+''p''</sub> = ''a''<sub>''n''</sub>
for all values of ''n''.<ref name=":0" /><ref>{{Cite web|last=Bosma|first=Wieb|title=Complexity of Periodic Sequences|url=https://www.math.ru.nl/~bosma/pubs/periodic.pdf|access-date=13 August 2021|website=www.math.ru.nl}}</ref><ref name=":2">{{Cite journal|last1=Janglajew|first1=Klara|last2=Schmeidel|first2=Ewa|date=2012-11-14|title=Periodicity of solutions of nonhomogeneous linear difference equations|journal=Advances in Difference Equations|volume=2012|issue=1|pages=195|doi=10.1186/1687-1847-2012-195|s2cid=122892501|issn=1687-1847|doi-access=free}}</ref> If a sequence is regarded as a [[function (mathematics)|function]] whose domain is the set of [[natural number]]s, then a periodic sequence is simply a special type of [[periodic function]].{{Citation needed|date=August 2021}} The smallest ''p'' for which a periodic sequence is ''p''-periodic is called its '''least period'''<ref name=":0" /> or '''exact period'''.