To appear suddenly in one's thoughts.
spring to mind
To appear suddenly in one's thoughts, often as an example of something …
come to mind
To appear in one's thoughts.
not leave one's thoughts
To remain in one's mind for a long duration.
on someone's mind
Preoccupying someone; present in someone's thoughts.
on one's mind
In one's thoughts, especially persistently or recurrently.
top of mind
Foremost in one's thoughts; of greatest concern or priority.