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.
In the following table, graphs with a(n) vertices and induced cycles of lengths 3..n are shown. The vertices 1, 2, ..., n constitute an induced cycle; only the additional vertices n+1, ..., a(n) and their lists of neighbors are given. n | a(n) | vertices outside the given induced n-cycle and their neighbors ---+------+--------------------------------------------------------------- 3 | 3 | none 4 | 5 | 5:1,2 5 | 6 | 6:1,2,4 6 | 7 | 7:1,2,4 7 | 9 | 8:1,2,4,9; 9:6,8 8 | 10 | 9:1,3,4,10; 10:6,9 9 | 11 | 10:1,5,11; 11:2,5,10 10 | 12 | 11:1,2,4,7; 12:6,9 11 | 13 | 12:1,2,5,6,8; 13:3,11 12 | 14 | 13:1,2,5,7; 14:3,6,8 13 | 16 | 14:1,3,4,7,15; 15:10,14; 16:6,9 For n = 7, the graph with a cycle 1-2-...-7-1 and two additional vertices with edges 8-1, 8-2, 8-4, 8-9, and 9-6 contains induced cycles of lengths 3..7: 1-2-8-1, 2-3-4-8-2, 1-7-6-9-8-1 (for example), 1-7-6-5-4-8-1, and 1-2-3-4-5-6-7-1. No such graph with fewer vertices exists, so a(7) = 9.
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