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I am fascinated by this entry OEIS A213253 which lists the smallest $k$ such that highest prime factor of $m(m+1)\dots(m+k-1)$ is $> n$ if $m > n$.

The article has references to the algorithm for generating this list.

Does anyone know of any recent work analyzing the upper or lower bounds for this sequence?

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Can you edit your question so the question is in the body and not just in the title? –  Gerry Myerson Sep 24 '12 at 23:11
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There may be something in Filip Najman, Large strings of consecutive smooth integers, Arch. Math. (Basel) 97 (2011), no. 4, 319–324. –  Gerry Myerson Sep 24 '12 at 23:16
    
Hi Gerry, I've edited the question so that the full information is in the body. I've read through Najman's paper and also M. Bauer and M. A. Bennett, Prime factors of consecutive integers, Math. Comp., 77 (2008), 2455-2459. –  Larry Freeman Sep 25 '12 at 1:10

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