%N Increasing gaps between squarefree numbers (upper end).
%C Up to n=10, a(n) is the upper end of the first gap of length n. However, for n=11 through n=16, a(n) is the upper end of the first gap of length n+1. See A020753. - _M. F. Hasler_, Dec 28 2015
%F a(n) = A020754(n) + A020753(n). - _M. F. Hasler_, Dec 28 2015
%e The first gap in A005117 occurs between 1 and 2 and has length 1. The next largest gap occurs between 3 and 5 and has length 2. The next largest gap is between 7 and 10 and has length 3. Etc. We are only interested in gaps that set new records.
%o (PARI) A020755(n)=for(k=L=1,9e9,issquarefree(k)||next;k-L>=n&&return(k);L=k) \\ _M. F. Hasler_, Dec 28 2015
%Y Cf. A005117, A020754, A020753, A045882, A051681.
%A _David W. Wilson_
%E Thanks to Christian Bower for additional comments.
%E More terms (computed using data from A020754) added by _M. F. Hasler_, Dec 28 2015