[seqfan] Is there any problems with this proof?

[John W. Nicholson]

Below is a proof based on A005250(n ) of the OEIS.  Can someone look at it and tell me if it true?
http://math.stackexchange.com/questions/1155523/is-frac-textnext-maximal-textmaximal-2-true
If it is true, an edit of A005250 comments is needed.  

Related:
https://math.stackexchange.com/questions/831768/under-assumption-that-fracm-n1m-n-le-2-what-is-true?lq=1
https://math.stackexchange.com/questions/793555/is-there-a-conjecture-with-maximal-prime-gaps?lq=1


 John W. Nicholson