P(4,1) is true because of 2,3,4,5 but I strongly doubt that P(5,1) is true. Indeed P(4,1) is only true that once and even P(3,1) happens for the last time at 7,8,9. Of any 210 consecutive integers one is divisible by 2,3,5,7 so P(210,3) fails. I'm sure that can be improved. It does generalize .
Aaron Meyerowitz
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