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.
%I A097501 #16 Sep 07 2019 09:05:08
%S A097501 368,94932,36314872537968,244552822542936127033092,
%T A097501 2177185942561672462146321298650240665136431700,
%U A097501 2246585380039521951243337580678537047744572047581514711375688196554564
%N A097501 p^q + q^p for twin primes p and q.
%C A097501 Except for the first term, 6 divides a(n). Let p = 3k+2 for odd k since k even implies p even, a contradiction. Then p = 6m + 5 and q = 6m+7 = 6m1 + 1. So p^q+q^p = (6m+5)^(6m1+1) + (6m1+1)^(6m+5) = 6H + 5^odd + 1^odd. Now 5 = (6-1) and (6-1)^odd + 1 = 6G -1 + 1 = 6G as stated. Are 3 and 17 the only primes in A051442(n)?
%e A097501 Consider the second twin prime pair (5,7). 5^7 + 7^5 = 94932, the 2nd entry.
%t A097501 lst={}; Do[p=Prime[n]; If[PrimeQ[q=p+2],a=(p^q+q^p); AppendTo[lst,a]],{n,2*4!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 16 2009 *)
%t A097501 #[[1]]^#[[2]]+#[[2]]^#[[1]]&/@Select[Partition[Prime[Range[20]],2,1],#[[2]] - #[[1]]==2&] (* _Harvey P. Dale_, Sep 07 2019 *)
%o A097501 (PARI) f(n) = for(x=1,n,p=prime(x);q=prime(x+1);if(q-p==2,v=p^q+q^p;print1(v",")))
%Y A097501 Cf. A051442.
%K A097501 nonn
%O A097501 2,1
%A A097501 _Cino Hilliard_, Aug 25 2004