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.
(See the program at A205402.)
s[n_] := s[n] = (1/2) Floor[(n + 1)^2/2];
z1 = 1000; z2 = 80;
Table[s[n], {n, 1, 30}] (* A002620, quarter-squares *)
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}] (* A205400 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]]
Table[d[n], {n, 1, z2}] (* A205401 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2]
m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2]
j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2
Table[k[n], {n, 1, z2}] (* A205402 *)
Table[j[n], {n, 1, z2}] (* A205403 *)
Table[s[k[n]], {n, 1, z2}] (* A205404 *)
Table[s[j[n]], {n, 1, z2}] (* A205405 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205406 *)
Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A198293 *)
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