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 A075673 #13 Feb 24 2023 12:15:24
%S A075673 4,15,45,111,232,422,704,1129,1667,2403,3287,4470,5810,7508,9414,
%T A075673 11663,14363,17454,20715,24739,29214,33957,39183,45540,52056,59497,
%U A075673 67181,75862,84831,95697,106608,117812,130356,143759,158617,174312,190500
%N A075673 Sum of next n integer interprimes (cf. A024675).
%C A075673 Sum of next n primes is A007468. Sum of next n odd interprimes is A075674. Sum of next n even interprimes is A075675.
%H A075673 Harvey P. Dale, <a href="/A075673/b075673.txt">Table of n, a(n) for n = 1..1000</a>
%e A075673 a(1) = (3+5)/2 = 4; a(2) = (5+7)/2+(7+11)/2 = 15; a(3) = (11+13)/2+(13+17)/2 +(17+19)/2 = 45.
%t A075673 (* sum of next n integer interprimes*) i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; Table[Sum[(Prime[i+2]+Prime[i+1])/2, {i, i1, i2}], {n, 1, 40}]
%t A075673 With[{nn=40},Total/@TakeList[Mean/@Partition[Prime[Range[2,(nn(nn+1))/2+2]],2,1],Range[nn]]] (* _Harvey P. Dale_, Feb 24 2023 *)
%Y A075673 Cf. A024675, A007468, A075673, A075674, A075675.
%K A075673 nonn
%O A075673 1,1
%A A075673 _Zak Seidov_, Sep 24 2002