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 A353198 #30 Jul 03 2022 09:24:17
%S A353198 13,37,52,61,73,97,109,117,148,157,169,181,193,208,229,241,244,277,
%T A353198 292,313,325,333,337,349,373,388,397,409,421,433,436,457,468,481,541,
%U A353198 549,577,592,601,613,628,637,657,661,673,676,709,724,733,757,769,772,793,829,832,853,873,877
%N A353198 Intersection of A000404 and A024614.
%C A353198 A000404 lists the numbers that are the squares of Euclidean distances between two lattice points on a square grid, the segment between which is not parallel to either axis, and thus the square grid could be divided into such number of parts symmetrically, periodically and nontrivially. Similarly, A024614 lists the numbers that are the squares of Euclidean distances between two lattice points on a hexagonal grid, the segment between which is not parallel to any of the axes.
%C A353198 Thus this sequence lists the numbers into which both the square grid and hexagonal one could be divided.
%C A353198 This sequence contains all the prime numbers of the form p = 12*k + 1 and, for each such prime, all composites of the form c = j^2*p.
%e A353198 The square grid (or the Gaussian integers) can be divided into 13 parts, where the k-th part consists of grid points of the form (k + 3*n + 2*m, 2*n - 3*m) where n, m are integers. Similarly the hexagonal grid can be also divided into 13 parts, where the k-th part consists of points of the form (k + 7/2*n + m, sqrt(3)/2*n + 2*sqrt(3)*m).
%t A353198 Select[Intersection[
%t A353198 Sort[DeleteDuplicates[
%t A353198 Flatten[Table[i^2 + j^2, {i, 1000}, {j, 1000}]]]],
%t A353198 Sort[DeleteDuplicates[
%t A353198 Flatten[Table[i^2 + i j + j^2, {i, 1000}, {j, 1000}]]]]], # <=
%t A353198 10000 &]
%Y A353198 Cf. A000404, A024614.
%K A353198 nonn
%O A353198 1,1
%A A353198 _Steven Lu_, May 16 2022