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 A357059 #48 Sep 29 2022 08:51:57
%S A357059 0,3,1,3,2,1,6,2,0,6,4,6
%N A357059 Decimal expansion of sum of squares of reciprocals of primes whose distance to the next prime is equal to 4, Sum_{j>=1} 1/A029710(j)^2.
%C A357059 Convergence table:
%C A357059 k A029710(k) Sum_{j=1..k} 1/A029710(j)^2
%C A357059 10000000 3285441223 0.031321620645456519799598611681
%C A357059 20000000 7067090263 0.031321620645890982910821292996
%C A357059 30000000 11044597393 0.031321620646019474620358985896
%C A357059 40000000 15153534937 0.031321620646079307404248696076
%C A357059 50000000 19360462153 0.031321620646113421819579063642
%C A357059 60000000 23647877233 0.031321620646135276227114122713
%C A357059 70000000 28000392817 0.031321620646150384406674037099
%e A357059 0.031321620646...
%t A357059 aa = {}; Do[g1[2 n] = 0, {n, 1, 1000}]; Do[g2[2 n] = 0, {n, 1, 1000}]; Do[g3[2 n] = 0, {n, 1, 1000}]; Do[g4[2 n] = 0, {n, 1, 1000}]; Do[g[2 n] = 0, {n, 1, 1000}];
%t A357059 w1 = 3; n = 3; Monitor[While[n < 10^10, w2 = NextPrime[w1]; kk = w2 - w1;
%t A357059 If[kk < 2000, g[kk] = g[kk] + 1; g1[kk] = g1[kk] + N[1/w1, 1000];g2[kk] = g2[kk] + N[1/w1^2, 1000];g3[kk] = g3[kk] + N[1/w1^3, 1000];g4[kk] = g4[kk] + N[1/w1^4, 1000];
%t A357059 If[IntegerQ[g[kk]/1000000], Print[{n, w1, kk, g[kk]}];If[kk == 4,AppendTo[aa, {n, w1, kk, g[kk], g1[kk], g2[kk], g3[kk], g4[kk]}]]]];w1 = w2; n++], n];aa
%Y A357059 Cf. A006512, A023200, A029710, A046132, A065421, A077800, A078437, A085548, A096247, A160910, A194098, A209328, A209329, A242301, A242302, A242303, A242304, A306539, A342714, A356793.
%K A357059 nonn,cons,hard,more
%O A357059 0,2
%A A357059 _Artur Jasinski_, Sep 10 2022