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=3;lst={};Do[p=Prime[n];If[PrimeQ[p=2^p-p*q],AppendTo[lst,p]],{n,5!}];lst
Select[2^#-3#&/@Prime[Range[900]],PrimeQ] (* Harvey P. Dale, Dec 09 2013 *)
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
a(3) = 61 is a term because 61 = 2^6 - 3 where 61 and 3 are prime and 6 is divisible by 3.
R:= NULL: count:= 0:
for k from 1 while count < 20 do
P:= sort(convert(numtheory:-factorset(k),list),`>`);
for p in P do
x:= 2^k-p;
if isprime(x) then R:= R,x; count:= count+1; fi
od od:
R;
8179 = 2^13 - 13
nn = 600000; mx = Floor[Log[2, nn]]; t2 = Select[Table[2^n - n, {n, Prime[Range[PrimePi[mx]]]}], PrimeQ]; mx = Floor[Sqrt[nn]]; tp = Select[Table[n^2 - 2, {n, Prime[Range[PrimePi[mx]]]}], PrimeQ]; Union[t2, tp] (* T. D. Noe, May 01 2012 *)
Module[{upto=350000,r},r=Floor[Sqrt[upto+2]];Select[Union[Select[ (#1[[1]]^#1[[2]]-#1[[2]]&)/@Tuples[Prime[Range[r]],2], PrimeQ]], #1<=upto&]] (* Harvey P. Dale, Dec 07 2012 *)
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
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