This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
q=5;lst={};Do[p=Prime[n];If[PrimeQ[p=2^p-p*q],AppendTo[lst,p]],{n,5!}];lst
Select[Table[2^p-5p,{p,Prime[Range[50]]}],PrimeQ] (* Harvey P. Dale, Jul 02 2018 *)
q=7;lst={};Do[p=Prime[n];If[PrimeQ[p=2^p-p*q],AppendTo[lst,p]],{n,5!}];lst
q=9;lst={};Do[p=Prime[n];If[PrimeQ[p=2^p-p*q],AppendTo[lst,p]],{n,5!}];lst
Select[2^#-9#&/@Prime[Range[50]],PrimeQ] (* Harvey P. Dale, Aug 26 2014 *)
q=15;lst={};Do[p=Prime[n];If[PrimeQ[p=2^p-p*q],AppendTo[lst,p]],{n,5!}];lst