BUG: period_range gives incorrect output

[abdulfatir]

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

start = pd.Period("2002-01-01 00:00", freq="30T")
print(
    pd.period_range(start=start, periods=5),
    pd.period_range(start=start, periods=5, freq=start.freq),
)

Issue Description

The code above outputs:

PeriodIndex(['2002-01-01 00:00', '2002-01-01 00:01', '2002-01-01 00:02',
             '2002-01-01 00:03', '2002-01-01 00:04'],
            dtype='period[30T]')
PeriodIndex(['2002-01-01 00:00', '2002-01-01 00:30', '2002-01-01 01:00',
             '2002-01-01 01:30', '2002-01-01 02:00'],
            dtype='period[30T]')

The two outputs are not the same. The default behavior when freq is not passed as an argument is incorrect.

Expected Behavior

By default period_range should use the start/end Period's freq as mentioned in the documentation but the output is incorrect.

Installed Versions

INSTALLED VERSIONS

commit : 965ceca
python : 3.9.16.final.0
python-bits : 64
OS : Linux
OS-release : 5.15.0-1033-aws
Version : #37~20.04.1-Ubuntu SMP Fri Mar 17 11:39:30 UTC 2023
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : C.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.0.2
numpy : 1.24.3
pytz : 2023.3
dateutil : 2.8.2
setuptools : 67.7.2
pip : 23.1.2
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 : 8.14.0
pandas_datareader: None
bs4 : 4.12.2
bottleneck : None
brotli : 1.0.9
fastparquet : None
fsspec : 2023.5.0
gcsfs : None
matplotlib : 3.7.1
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 8.0.0
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : 1.10.1
snappy : None
sqlalchemy : None
tables : None
tabulate : 0.9.0
xarray : 2023.5.0
xlrd : None
zstandard : None
tzdata : 2023.3
qtpy : None
pyqt5 : None

[jayendra-patil33]

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