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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Consecutive integers divisible by a set of Primes

**Physics Forums | Science Articles, Homework Help, Discussion**