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.
The irregular triangle T(n,k) begins: n\ k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ... K 2 4 6 8 10 12 14 ... ----------------------------------------------------------------------------- 2: 0 1 3: 1 0 4: 2 1 2 1 5: 3 2 3 2 6: 6 6 7 4 6 6 7: 8 8 9 6 8 8 8: 14 19 18 21 19 17 18 21 9: 25 24 31 27 30 21 31 27 10: 36 36 51 52 49 39 51 52 43 43 11: 41 41 59 59 54 44 59 59 48 48 12: 189 190 286 283 253 268 307 309 266 262 222 220 13: 209 211 315 313 282 296 340 342 287 282 245 243 14: 257 257 462 459 433 448 489 488 394 391 372 367 394 391 15: 542 550 996 990 843 910 1019 1083 992 1044 757 800 824 810 ... ------------------------------------------------------------------------------- n = 2: The 1 = A348842(2) game JG(2) is [2, 1], with an even number of moves (B wins); hence row n = 2 is 0, 1, because there is no game with an odd number of moves. Thus JG(2) is called secondary. n = 4: The 6 games JG(4) are: [2, 1, 3], [2, 1, 4] and [2, 4, 1, 3] for K = 2, and [4, 1, 2], [4, 1, 3] and [4, 2, 1, 3], for K = 4; hence row n = 4 gives 2, 1, for K = 2 as well as for K = 4. This means that in these six games A wins four times and B twice. But B can always win by reacting on 2 with 4, and on 4 with 2, leading to [2, 4, 1, 3] and [4, 2, 1, 3]. Thus the game JG(4) is called secondary. n = 6: There are 35 games, A wins 19 times and B 16 times. For K = 2 and K = 6 6 times A, 6 times B, and for K = 4 4 times A and 7 times B. Again B is a safe winner reacting to K = 2 with 4 ([2, 4, 1, 5] or [2, 4, 1, 3]), to K = 4 with 2, then 5 ([4, 2, 1, 5]), and to K = 6 with 3 then 5 ([6, 3, 1, 5]). Thus JG(6) is also secondary. n = 9: There are 216 games, A wins 117 times and B 99 times. There is a strategy for B, and JG(9) is secondary.
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