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 A114379 #12 Apr 01 2015 16:27:45
%S A114379 23,41,109,187,349,551,841,1079,1667,1779,2357,2599,3219,3487,3631,
%T A114379 4319,4533,5197,5501,6213,7039,8709,9031,9829,11233,12425,13227,13677,
%U A114379 14329,14813,18667,18951,19073,19973,20561,24329,24685,25153,25561,26261
%N A114379 Sums of p-th to the q-th prime where p and q are twin primes.
%C A114379 Conjecture: The number of terms in this sequence is infinite.
%H A114379 Danny Rorabaugh, <a href="/A114379/b114379.txt">Table of n, a(n) for n = 1..10000</a>
%F A114379 prime(k) = A000040(k) is the k-th prime number.
%F A114379 a(n) = Sum_{k=A077800(2n-1)..A077800(2n)} prime(k). - _Danny Rorabaugh_, Apr 01 2015
%e A114379 3 and 5 are the first twin prime pair: prime(3) = 5, prime(4) = 7, prime(5) = 11
%e A114379 and 5+7+11 = 23, the first entry in the table.
%t A114379 Plus @@ (Prime /@ Range[#, # + 2]) & /@ Select[Prime@ Range@ 200, PrimeQ[# + 2] &] (* _Michael De Vlieger_, Apr 01 2015 *)
%o A114379 (PARI) sumprimes(m, n) = { local(x); return(sum(x=m, n, prime(x))) }
%o A114379 g(n)=forprime(x=3,n,if(isprime(x+2),print1(sumprimes(x,x+2)",")))
%K A114379 easy,nonn
%O A114379 1,1
%A A114379 _Cino Hilliard_, Feb 10 2006