I think it's important to note that "Ketogenic" might not be the right word for the necessary diet intervention to make it easier to fast for long periods.

Ketosis is a state where you eat so little carbohydrate, that your body is forced to create "ketone bodies" to fuel the brain. This typically happens at <50g/day carbohydrate.

Most anecdotal evidence (and my own experiences) show that you can get your body into a primarily fat-burning state that makes it easier to fast for long periods without hunger pangs by eating up to somewhere around 100 or 150g/day carbohydrate (assuming you eat a 2000-2500 Kcal/day diet) while providing enough glucose to the brain that your body is not forced to create excess Ketone bodies.