Exercises in octaves on the piano
A player with a sufficiently large hand may use the third finger in the following exercises.

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How to play connected octaves : piano exercises
Fingering to be used when playing them slowly
When playing octaves the performer should connect them as much as possible by a skillful gliding of the thumb and fingers, using the 3d and 4th fingers on the black key as well as by passing the 3d and 4th fingers over the 5th.