Yes "the continuity of residence" is required for naturalization.
> An applicant for naturalization ... must have resided continuously in the United States after his or her lawful permanent resident (LPR) admission for at least 5 years prior to filing the naturalization application and up to the time of naturalization.
> An applicant for naturalization ... must have resided continuously in the United States after his or her lawful permanent resident (LPR) admission for at least 5 years prior to filing the naturalization application and up to the time of naturalization.