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 A078731 #9 Apr 06 2025 08:45:32
%S A078731 0,0,0,23,37,100,67,348,0,371,0,660,0,0,434,233,771,277,600,985,3810,
%T A078731 0,1788,3435,2208,1757,1220,631,1300,13190,0,0,1692,1740,16239,0,1039,
%U A078731 0,2156,6678,10749,3745,1283,1297,1307,11040,4319,2930,0,23259,1613,6584
%N A078731 Sum of primes between successive pairs of twin primes.
%H A078731 Amiram Eldar, <a href="/A078731/b078731.txt">Table of n, a(n) for n = 1..10000</a>
%e A078731 Between the 8th and 9th pairs of twin primes are 4 primes: (71,73) 79 83 89 97 (101,103), therefore a(8) = 79+83+89+97 = 348.
%t A078731 seq[lim_] := Module[{p = Prime[Range[lim]], d, i}, d = Differences[p]; i = Position[d, 2] // Flatten; If[First[#] + 2 >= Last[#], 0, Total[p[[First[#] + 2 ;; Last[#] - 1]]]] & /@ Partition[i, 2, 1]]; seq[300] (* _Amiram Eldar_, Apr 06 2025 *)
%Y A078731 Cf. A001097, A048614.
%K A078731 nonn
%O A078731 1,4
%A A078731 _Reinhard Zumkeller_, Dec 20 2002