I am having more than a little fun with this sequence of numbers and am looking for a better algorithm to find the next numbers in the sequence.(adsbygoogle = window.adsbygoogle || []).push({});

Let Z be the set of the first n odd primes. Find two integers j and k that are relatively prime to all members of Z where every integer between j and k is not relatively prime to all members of Z. The absolute value of j-k must be the maximum value possible. This maximum value I call frg(n).

So, for the set with only {3} |4-2| = 2 4 and 2 are relatively prime to 3, but 3 is not.

For the set {3,5} |7-4| = 3 7 and 4 are relatively prime to 3 and 5, but 5 and 6 are not.

frg(1) = 2, frg(2) = 3, frg(3) = 5, frg(4) = 11, ..... frg(8) = 20

I initially thought this would just be the sequence of primes but it is not. Now I wonder how weird it gets as we go out the sequence.

I can get to frg(15) with my desktop. I know someone can do better!

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# Consecutive integers divisible by a set of Primes

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