I may have found something in this data involving:

http://www.research.att.com/~njas/sequences/A176260 as it's one of the sequences as far as I can see and maybe I we can find a way to like the Mersenne prime exponents to Fibonacci numbers through->

http://www.research.att.com/~njas/sequences/A047264
just a guess anyone else want to see if it's useful ?