diff --git a/adaptive/learner/sequence_learner.py b/adaptive/learner/sequence_learner.py
index 2f7a34171..c307744fd 100644
--- a/adaptive/learner/sequence_learner.py
+++ b/adaptive/learner/sequence_learner.py
@@ -2,7 +2,7 @@
 
 import sys
 from copy import copy
-from typing import Any
+from typing import TYPE_CHECKING, Any
 
 import cloudpickle
 from sortedcontainers import SortedDict, SortedSet
@@ -15,6 +15,10 @@
     partial_function_from_dataframe,
 )
 
+if TYPE_CHECKING:
+    from collections.abc import Sequence
+    from typing import Callable
+
 try:
     import pandas
 
@@ -82,12 +86,17 @@ class SequenceLearner(BaseLearner):
     the added benefit of having results in the local kernel already.
     """
 
-    def __init__(self, function, sequence):
+    def __init__(
+        self,
+        function: Callable[[Any], Any],
+        sequence: Sequence[Any],
+    ):
         self._original_function = function
         self.function = _IgnoreFirstArgument(function)
         # prefer range(len(...)) over enumerate to avoid slowdowns
         # when passing lazy sequences
-        self._to_do_indices = SortedSet(range(len(sequence)))
+        indices = range(len(sequence))
+        self._to_do_indices = SortedSet(indices)
         self._ntotal = len(sequence)
         self.sequence = copy(sequence)
         self.data = SortedDict()
@@ -161,6 +170,8 @@ def to_dataframe(  # type: ignore[override]
         index_name: str = "i",
         x_name: str = "x",
         y_name: str = "y",
+        *,
+        full_sequence: bool = False,
     ) -> pandas.DataFrame:
         """Return the data as a `pandas.DataFrame`.
 
@@ -178,6 +189,9 @@ def to_dataframe(  # type: ignore[override]
             Name of the input value, by default "x"
         y_name : str, optional
             Name of the output value, by default "y"
+        full_sequence : bool, optional
+            If True, the returned dataframe will have the full sequence
+            where the y_name values are pd.NA if not evaluated yet.
 
         Returns
         -------
@@ -190,8 +204,16 @@ def to_dataframe(  # type: ignore[override]
         """
         if not with_pandas:
             raise ImportError("pandas is not installed.")
-        indices, ys = zip(*self.data.items()) if self.data else ([], [])
-        sequence = [self.sequence[i] for i in indices]
+        import pandas as pd
+
+        if full_sequence:
+            indices = list(range(len(self.sequence)))
+            sequence = list(self.sequence)
+            ys = [self.data.get(i, pd.NA) for i in indices]
+        else:
+            indices, ys = zip(*self.data.items()) if self.data else ([], [])  # type: ignore[assignment]
+            sequence = [self.sequence[i] for i in indices]
+
         df = pandas.DataFrame(indices, columns=[index_name])
         df[x_name] = sequence
         df[y_name] = ys
@@ -209,6 +231,8 @@ def load_dataframe(  # type: ignore[override]
         index_name: str = "i",
         x_name: str = "x",
         y_name: str = "y",
+        *,
+        full_sequence: bool = False,
     ):
         """Load data from a `pandas.DataFrame`.
 
@@ -231,10 +255,25 @@ def load_dataframe(  # type: ignore[override]
             The ``x_name`` used in ``to_dataframe``, by default "x"
         y_name : str, optional
             The ``y_name`` used in ``to_dataframe``, by default "y"
+        full_sequence : bool, optional
+            The ``full_sequence`` used in ``to_dataframe``, by default False
         """
+        if not with_pandas:
+            raise ImportError("pandas is not installed.")
+        import pandas as pd
+
         indices = df[index_name].values
         xs = df[x_name].values
-        self.tell_many(zip(indices, xs), df[y_name].values)
+        ys = df[y_name].values
+
+        if full_sequence:
+            evaluated_indices = [i for i, y in enumerate(ys) if y is not pd.NA]
+            xs = xs[evaluated_indices]
+            ys = ys[evaluated_indices]
+            indices = indices[evaluated_indices]
+
+        self.tell_many(zip(indices, xs), ys)
+
         if with_default_function_args:
             self.function = partial_function_from_dataframe(
                 self._original_function, df, function_prefix
diff --git a/adaptive/tests/test_sequence_learner.py b/adaptive/tests/test_sequence_learner.py
index fdd3dcb10..9ef5a8f14 100644
--- a/adaptive/tests/test_sequence_learner.py
+++ b/adaptive/tests/test_sequence_learner.py
@@ -1,7 +1,17 @@
 import asyncio
 
+import pytest
+
 from adaptive import Runner, SequenceLearner
-from adaptive.runner import SequentialExecutor
+from adaptive.learner.learner1D import with_pandas
+from adaptive.runner import SequentialExecutor, simple
+
+offset = 0.0123
+
+
+def peak(x, offset=offset, wait=True):
+    a = 0.01
+    return {"x": x + a**2 / (a**2 + (x - offset) ** 2)}
 
 
 class FailOnce:
@@ -22,3 +32,27 @@ def test_fail_with_sequence_of_unhashable():
     runner = Runner(learner, retries=1, executor=SequentialExecutor())
     asyncio.get_event_loop().run_until_complete(runner.task)
     assert runner.status() == "finished"
+
+
+@pytest.mark.skipif(not with_pandas, reason="pandas is not installed")
+def test_save_load_dataframe():
+    learner = SequenceLearner(peak, sequence=range(10, 30, 1))
+    simple(learner, npoints_goal=10)
+    df = learner.to_dataframe()
+    assert len(df) == 10
+    assert df["x"].iloc[0] == 10
+    df_full = learner.to_dataframe(full_sequence=True)
+    assert len(df_full) == 20
+    assert df_full["x"].iloc[0] == 10
+    assert df_full["x"].iloc[-1] == 29
+
+    learner2 = learner.new()
+    assert learner2.data == {}
+    learner2.load_dataframe(df)
+    assert len(learner2.data) == 10
+    assert learner.to_dataframe().equals(df)
+
+    learner3 = learner.new()
+    learner3.load_dataframe(df_full, full_sequence=True)
+    assert len(learner3.data) == 10
+    assert learner3.to_dataframe(full_sequence=True).equals(df_full)