BUG: .to_json() of periode_range gives OverflowError: Maximum recursion level reached

[IbHansen]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import pandas as pd
pd.Series(pd.period_range(start=2021,freq = 'Y',periods=3)).to_json()

### Issue Description

causes a: OverflowError: Maximum recursion level reached
 the same goes if a periode_range is a column in a dataframe 

### Expected Behavior

should return: 
'{"0":{"day":31,"day_of_week":4,"day_of_year":365,"dayofweek":4,"dayofyear":365,"days_in_month":31,"daysinmonth":31,"end_time":1640995199999,"freqstr":"A-DEC","hour":0,"is_leap_year":false,"minute":0,"month":12,"ordinal":51,"quarter":4,"qyear":2021,"second":0,"start_time":1609459200000,"week":52,"weekday":4,"weekofyear":52,"year":2021},"1":{"day":31,"day_of_week":5,"day_of_year":365,"dayofweek":5,"dayofyear":365,"days_in_month":31,"daysinmonth":31,"end_time":1672531199999,"freqstr":"A-DEC","hour":0,"is_leap_year":false,"minute":0,"month":12,"ordinal":52,"quarter":4,"qyear":2022,"second":0,"start_time":1640995200000,"week":52,"weekday":5,"weekofyear":52,"year":2022},"2":{"day":31,"day_of_week":6,"day_of_year":365,"dayofweek":6,"dayofyear":365,"days_in_month":31,"daysinmonth":31,"end_time":1704067199999,"freqstr":"A-DEC","hour":0,"is_leap_year":false,"minute":0,"month":12,"ordinal":53,"quarter":4,"qyear":2023,"second":0,"start_time":1672531200000,"week":52,"weekday":6,"weekofyear":52,"year":2023}}'

### Installed Versions

<details>

INSTALLED VERSIONS
------------------
commit              : e86ed377639948c64c429059127bcf5b359ab6be
python              : 3.10.12.final.0
python-bits         : 64
OS                  : Windows
OS-release          : 10
Version             : 10.0.22621
machine             : AMD64
processor           : Intel64 Family 6 Model 140 Stepping 1, GenuineIntel
byteorder           : little
LC_ALL              : None
LANG                : None
LOCALE              : Danish_Denmark.1252

pandas              : 2.1.1
numpy               : 1.26.0
pytz                : 2023.3.post1
dateutil            : 2.8.2
setuptools          : 68.2.2
pip                 : 23.2.1
Cython              : None
pytest              : None
hypothesis          : None
sphinx              : None
blosc               : None
feather             : None
xlsxwriter          : None
lxml.etree          : None
html5lib            : None
pymysql             : None
psycopg2            : None
jinja2              : 3.1.2
IPython             : 8.16.1
pandas_datareader   : None
bs4                 : 4.12.2
bottleneck          : None
dataframe-api-compat: None
fastparquet         : None
fsspec              : None
gcsfs               : None
matplotlib          : None
numba               : None
numexpr             : None
odfpy               : None
openpyxl            : None
pandas_gbq          : None
pyarrow             : None
pyreadstat          : None
pyxlsb              : None
s3fs                : None
scipy               : None
sqlalchemy          : None
tables              : None
tabulate            : None
xarray              : None
xlrd                : None
zstandard           : None
tzdata              : 2023.3
qtpy                : None
pyqt5               : None
</details>

[lithomas1]

Hi and thanks for reporting this issue, I can confirm that this issue still exists on main.

This might be a duplicate of #31917, even though the error message has changed a bit.

[xiaohuanlin]

take

[xiaohuanlin]

I investigated this error and found it was introduced by this PR: #23915
The root cause is it's the new object with the same class when iterating the attributes of a object. In this issue, the special attribute is base and will return the same offset object with a base attribute.
I wonder if I can change the name of this attribute from base to _base. It will prevent iterating this attribute.

[Aloqeely]

I can still reproduce this on main, this error is really misleading.
If this is not going to be fixed anytime soon we should at least consider raising a TypeError instead