Arithmetic Frobenius

I have an unlimited supply of 17-cent, 18-cent, and 19-cent stamps. I'd like to put exactly \( N \) cents' worth of postage on an envelope, but no matter which combination of stamps I try, I am unable to accomplish this.

What is the largest possible value of \( N \)?

Bonus 1: Generalize to any three consecutive integers.
Bonus 2: Generalize to any three-term arithmetic progression.
Bonus 3: Generalize to any arithmetic progression.


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