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 A333839 #17 Apr 28 2020 00:13:51
%S A333839 0,0,0,1,2,2,1,0,0,1,2,2,1,0,0,1,2,2,1,2,4,5,5,4,2,0,0,2,4,5,5,4,2,1,
%T A333839 2,2,1,0,0,1,2,2,1,2,4,5,5,4,2,2,4,5,5,4,2,0,0,2,4,5,5,4,2,1,2,2,1,0,
%U A333839 0,2,4,5,5,4,2,1,2,2,1,2,4,5,5,4,2,3,6,8,9,9,8,6
%N A333839 a(n) = Sum_{k = 4..n} ((prevprime(k) + nextprime(k))/2 - k).
%C A333839 It looks like a(n) >= 0 for all n >= 4.
%C A333839 If (n,n+2) are twin primes, then a(n) = 0 and a(n+1) = 0.
%C A333839 Partial sums of b(k) = prevprime(k) + nextprime(k) - 2*k; b(k) = 0 for A145025.
%F A333839 a(n) = Sum_{k = 4..n} (A013632(k) - A049711(k)) / 2.
%e A333839 a(4) = (3 + 5)/2 - 4 = 0;
%e A333839 a(5) = (3 + 5)/2 - 4 + (3 + 7)/2 - 5 = 0.
%t A333839 Array[Sum[Total[NextPrime[k, {-1, 1}]]/2 - k, {k, 4, #}] &, 92, 4] (* _Michael De Vlieger_, Apr 10 2020 *)
%Y A333839 Cf. A013632, A033559, A049711, A145025.
%K A333839 nonn
%O A333839 4,5
%A A333839 _Ctibor O. Zizka_, Apr 07 2020