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 A358312 #5 Nov 17 2022 07:20:26
%S A358312 3343,42293,461393,70793,72053,268267,8917219
%N A358312 Consider the graph of symmetric primes where p and q are connected if |p-q| = gcd(p-1,q-1). This sequence is an irregular table where the n-th row lists the first symmetric prime in a connected component with n vertices, with one representative for each nonisomorphic graph. Within a row, graphs are ordered by increasing size of its initial prime.
%C A358312 Row lengths are A001349(n); if the sequence is finite the last row may be shorter.
%C A358312 Kalmynin gives T(2, 1) = 3343 and proves that, under a conjecture which is intermediate between Dickson's conjecture and the Bateman-Horn-Stemmler conjecture, that this sequence is infinite.
%H A358312 A. B. Kalmynin, <a href="http://math.colgate.edu/~integers/v2/v2.pdf">On the Symmetry Graph of Prime Numbers</a>, INTEGERS 21 (2021), #A2.
%e A358312 T(2, 1) = 3343 has components {3343, 4457} which form the complete graph K_2.
%e A358312 T(3, 1) = 42293 has components {42293, 42487, 63439} which form the path graph P_3.
%e A358312 T(3, 2) = 461393 has components {461393, 519067, 692089} which form the complete graph K_3.
%e A358312 T(4, 1) = 70793 has components {70793, 106187, 106189, 123887} which form the claw graph.
%e A358312 T(4, 2) = 72053 has components {72053, 108079, 216157, 288209} which form the path graph P_4.
%e A358312 T(4, 3) = 268267 has components {268267, 357689, 536531, 536533} which form the paw graph.
%e A358312 T(4, 4) = 8917219 has components {8917219, 9908021, 14862031, 17834437} which form the square graph.
%Y A358312 Cf. A090190.
%K A358312 nonn,tabf,hard,more
%O A358312 2,1
%A A358312 _Charles R Greathouse IV_, Nov 08 2022