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BUG: DatetimeIndex.is_year_start breaks for business-day frequency where n is greater than 1 #58524

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@MarcoGorelli

Description

@MarcoGorelli
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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

In [68]: dr = pd.date_range("2017-01-01", periods=2, freq="B")

In [69]: dr
Out[69]: DatetimeIndex(['2017-01-02', '2017-01-03'], dtype='datetime64[ns]', freq='B')

In [70]: dr.is_year_start
Out[70]: array([ True, False])

In [71]: dr = pd.date_range("2017-01-01", periods=2, freq="2B")

In [72]: dr
Out[72]: DatetimeIndex(['2017-01-02', '2017-01-04'], dtype='datetime64[ns]', freq='2B')

In [73]: dr.is_year_start
Out[73]: array([False, False])

Issue Description

'2017-01-02' is recognised as year-start in one case, but not in the other

This hacky line is probably to blame

is_business = freqstr[0] == "B"

If anyone submits a fix, you probably want to parse the n and freq components of the offset, rather than messing around with freqstr

Expected Behavior

both return the same result

Installed Versions

INSTALLED VERSIONS

commit : d9cdd2e
python : 3.11.9.final.0
python-bits : 64
OS : Linux
OS-release : 5.15.146.1-microsoft-standard-WSL2
Version : #1 SMP Thu Jan 11 04:09:03 UTC 2024
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : C.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.2.2
numpy : 1.26.4
pytz : 2024.1
dateutil : 2.9.0.post0
setuptools : 65.5.0
pip : 24.0
Cython : None
pytest : 8.1.1
hypothesis : 6.100.1
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.3
IPython : 8.23.0
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.12.3
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : 2024.3.1
gcsfs : None
matplotlib : 3.8.4
numba : 0.59.1
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 15.0.2
pyreadstat : None
python-calamine : None
pyxlsb : None
s3fs : None
scipy : 1.13.0
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
zstandard : None
tzdata : 2024.1
qtpy : None
pyqt5 : None

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