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 A065117 #13 Sep 03 2018 19:10:08
%S A065117 3,113,463,593,743,1109,2473,4139,4657,4937,5531,5879,6473,6581,6659,
%T A065117 6701,7297,7529,8387,8521,8929,9349,10369,10499,12289,12829,13411,
%U A065117 13697,14033,14323,15907,18637,19391,19841,21143,21647,23021,27077
%N A065117 Primes such that prime(p) +- pi(p) are simultaneously prime.
%C A065117 Intersection of A065059 and A065060.
%H A065117 Harry J. Smith, <a href="/A065117/b065117.txt">Table of n, a(n) for n = 1..1000</a>
%e A065117 113 is in the sequence because PrimePi(113) is 30, Prime(113) is 617, and both 587 and 647 are primes.
%t A065117 Do[p0 = Prime[ Prime[n]]; p1 = PrimePi[ Prime[n]]; If[ PrimeQ[p0 + p1] && PrimeQ[p0 - p1], Print[ Prime[n]]], {n, 1, 5000} ]
%t A065117 spQ[n_]:=Module[{p=PrimePi[n]},AllTrue[Prime[n]+{p,-p},PrimeQ]]; Select[ Prime[ Range[10000]],spQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 03 2018 *)
%o A065117 (PARI) { n=0; default(primelimit, 4294965247); for (m=1, 10^9, p=prime(m); p0 = prime(p); p1 = primepi(p); if (isprime(p0 + p1) && isprime(p0 - p1), write("b065117.txt", n++, " ", p); if (n==1000, return)) ) } \\ _Harry J. Smith_, Oct 10 2009
%Y A065117 Cf. A065059, A065060.
%K A065117 nonn
%O A065117 1,1
%A A065117 _Robert G. Wilson v_, Nov 12 2001
%E A065117 Example corrected by _Harvey P. Dale_, Sep 03 2018