Consecutive Squarefrees, Not Coprime

[Jud McCranie]

At 09:09 PM 8/24/2005, Jud McCranie wrote:

>I've found that with high probability, a(6) = 9216772051242   (and its 
>partner is  9216772051254).  At this point I can't be sure that there 
>isn't a smaller one, but there probably isn't a smaller one.  Soon I hope 
>to have either a proof that it is the smallest (very likely it is) or 
>possibly find a smaller one.

A revised program has shown that indeed a(6)=9216772051242.  The next 
squarefree term is  9216772051254 and they have gcd 6.  (Anciently the 
program also shows that there are no terms for a(6n) less than this number.)

My thanks go to David Wilson and Don Reble for the solutions they 
found.  They help put a limit on searches as well as provide test cases.