CLN: PeriodIndex to use nan related cache
- [x] no tests added (all cases look to be covered) / passed
- [x] passes `git diff upstream/master | flake8 --diff`

## [Current coverage](https://codecov.io/gh/pydata/pandas/pull/13975?src=pr) is 85.26% (diff: 100%)

> Merging [#13975](https://codecov.io/gh/pydata/pandas/pull/13975?src=pr) into [master](https://codecov.io/gh/pydata/pandas/branch/master?src=pr) will decrease coverage by **<.01%**

``` diff
@@             master     #13975   diff @@
==========================================
  Files           139        139          
  Lines         50219      50216     -3   
  Methods           0          0          
  Messages          0          0          
  Branches          0          0          
==========================================
- Hits          42819      42816     -3   
  Misses         7400       7400          
  Partials          0          0          
```

> Powered by [Codecov](https://codecov.io?src=pr). Last update [4a80521...60b3351](https://codecov.io/gh/pydata/pandas/compare/4a805216d99b37955c97625d304980eff10cab56...60b3351e56c93a43468210345bb007c7d2304ba6?src=pr)
 Looks good to me!
 thanks!
