Is it safe to take ibuprofen right after taking prednisone?

Certainly if you have a history of stomach problems prednisone and ibuprofen should be used cautiously together, as they both can irritate the gastric lining and cause serious gastric problems.
This is not always the case though.
You can limit your risk by taking the tablets with a meal.

If you were to experience any side effects such as unusual bleeding, stomach pain, tarry stools or dizziness then you should tell your doctor immediately. Sometimes the Doctor may be another medication to help protect the stomach with the ibuprofen.

Make sure your doctor is aware of your history.
If you are concerned please talk to your Doctor to voice your concerns.

For more information see:
https://www.drugs.com/interactions-check.php?drug_list=1310-0,1933-0&types[]=major&types[]=minor&types[]=moderate&types[]=food&types[]=therapeutic_duplication