An integer is called p-smooth for a given prime p, if its prime factors don't exceed p. Sometimes a few consecutive integers are p-smooth (of course, we are interested in non-trivial cases, where the smallest integer in the chain exceeds the prime next to p): for example, 4374 and 4375 are 7-smooth, while 2430, 2431 and 2432 are 19-smooth. There are also some chains of larger length (all 41-smooth):

212380, 212381, 212382

1517, 1518, 1519, 1520, 1521

285, 286, 287, 288, 289, 290

Another six integers, from 3294850 to 3294855, are 239-smooth. Eight integers from 4895 to 4902 are 89-smooth, while 15 integers from 48503 ti 48517 are 379-smooth.

The case of two consecutive integers was already studied (Sloane's A002072, A145605), but there are little information about larger chains. It there any interesting results known?

Thanks,

Andrey

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