BUG: RangeIndex concatenating incorrectly a single object of length 1

doc/source/whatsnew/v1.3.0.rst

@@ -294,6 +294,7 @@ Indexing
 - Bug in setting ``timedelta64`` values into numeric :class:`Series` failing to cast to object dtype (:issue:`39086`)
 - Bug in setting :class:`Interval` values into a :class:`Series` or :class:`DataFrame` with mismatched :class:`IntervalDtype` incorrectly casting the new values to the existing dtype (:issue:`39120`)
 - Bug in incorrectly raising in :meth:`Index.insert`, when setting a new column that cannot be held in the existing ``frame.columns``, or in :meth:`Series.reset_index` or :meth:`DataFrame.reset_index` instead of casting to a compatible dtype (:issue:`39068`)
+- Bug in :meth:`RangeIndex.append` where a single object of length 1 was concatenated incorrectly (:issue:`39401`)
 
 Missing
 ^^^^^^^

pandas/core/indexes/range.py

@@ -697,6 +697,9 @@ def _concat(self, indexes, name):
         if not all(isinstance(x, RangeIndex) for x in indexes):
             return super()._concat(indexes, name)
 
+        elif len(indexes) == 1:
+            return indexes[0]
+
         start = step = next_ = None
 
         # Filter the empty indexes

pandas/tests/indexes/ranges/test_range.py

@@ -506,3 +506,18 @@ def test_format_empty(self):
         empty_idx = self._holder(0)
         assert empty_idx.format() == []
         assert empty_idx.format(name=True) == [""]
+
+    @pytest.mark.parametrize(
+        "RI",
+        [
+            RangeIndex(0, -1, -1),
+            RangeIndex(0, 1, 1),
+            RangeIndex(1, 3, 2),
+            RangeIndex(0, -1, -2),
+            RangeIndex(-3, -5, -2),
+        ],
+    )
+    def test_append_len_one(self, RI):
+        # GH39401
+        result = RI.append([])
+        tm.assert_index_equal(result, RI, exact=True)

pandas/tests/reshape/concat/test_series.py

@@ -143,3 +143,9 @@ def test_concat_series_partial_columns_names(self):
         result = concat([foo, bar, baz], axis=1, ignore_index=True)
         expected = DataFrame({0: [1, 2], 1: [1, 2], 2: [4, 5]})
         tm.assert_frame_equal(result, expected)
+
+    def test_concat_series_length_one_reversed(self, frame_or_series):
+        # GH39401
+        obj = frame_or_series([100])
+        result = pd.concat([obj.iloc[::-1]])
+        tm.assert_equal(result, obj)