Consider the strings $(b,b+1,b+2,...,b+l)$ of consecutive natural numbers, all less than some fixed natural number $n > b+l$. Is there a way to find the longest string (length of a string $= l+1$) with $\gcd(b+i,n) > 1$ for all $0\le i \le l$?
"Strings" of consecutive natural numbers
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number-theory
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1Search " Jacobsthal function" on Google or the OEIS. – 2012-10-11