BUG: Index[offset_objects] + Period (#50282)

Author: jbrockmendel

doc/source/whatsnew/v2.0.0.rst

@@ -895,6 +895,7 @@ I/O
 Period
 ^^^^^^
 - Bug in :meth:`Period.strftime` and :meth:`PeriodIndex.strftime`, raising ``UnicodeDecodeError`` when a locale-specific directive was passed (:issue:`46319`)
+- Bug in adding a :class:`Period` object to an array of :class:`DateOffset` objects incorrectly raising ``TypeError`` (:issue:`50162`)
 -
 
 Plotting

pandas/_libs/tslibs/period.pyx

@@ -1741,6 +1741,11 @@ cdef class _Period(PeriodMixin):
             raise TypeError(f"unsupported operand type(s) for +: '{sname}' "
                             f"and '{oname}'")
 
+        elif util.is_array(other):
+            if other.dtype == object:
+                # GH#50162
+                return np.array([self + x for x in other], dtype=object)
+
         return NotImplemented
 
     def __radd__(self, other):
@@ -1767,11 +1772,22 @@ cdef class _Period(PeriodMixin):
         elif other is NaT:
             return NaT
 
+        elif util.is_array(other):
+            if other.dtype == object:
+                # GH#50162
+                return np.array([self - x for x in other], dtype=object)
+
         return NotImplemented
 
     def __rsub__(self, other):
         if other is NaT:
             return NaT
+
+        elif util.is_array(other):
+            if other.dtype == object:
+                # GH#50162
+                return np.array([x - self for x in other], dtype=object)
+
         return NotImplemented
 
     def asfreq(self, freq, how="E") -> "Period":

pandas/tests/arithmetic/test_object.py

@@ -73,6 +73,18 @@ def test_more_na_comparisons(self, dtype):
 
 
 class TestArithmetic:
+    def test_add_period_to_array_of_offset(self):
+        # GH#50162
+        per = pd.Period("2012-1-1", freq="D")
+        pi = pd.period_range("2012-1-1", periods=10, freq="D")
+        idx = per - pi
+
+        expected = pd.Index([x + per for x in idx], dtype=object)
+        result = idx + per
+        tm.assert_index_equal(result, expected)
+
+        result = per + idx
+        tm.assert_index_equal(result, expected)
 
     # TODO: parametrize
     def test_pow_ops_object(self):