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 A351630 #84 Jun 02 2022 10:30:42 %S A351630 0,12,1270,105161 %N A351630 Nim values that occur at infinitely many heap sizes in the combinatorial game Mem0. %C A351630 The impartial combinatorial game Mem0 (aka Short Local Nim) is played with heaps of tokens, as in Nim. On each turn, k tokens may be removed from a heap H, provided that k is not equal to the number of tokens that were removed on the immediately preceding move on H. %C A351630 A heap may be denoted by n_k, where n is the number of tokens remaining and k the number removed on the preceding move. There are many nim values m that occur at just finitely many heap sizes, in the sense that G(n_k) = m for just finitely many choices of n. This sequence gives the exceptional values of m that occur at infinitely many heap sizes. %C A351630 It is unknown whether there are infinitely many such m. It is remarkable that such simple, parameterless rules give rise to an unusual and mysterious integer sequence. %D A351630 R. K. Guy and R. J. Nowakowski, Unsolved Problems in Combinatorial Games, More Games of No Chance, MSRI Publications, Volume 42, 2002, pp. 457-473, problem 22. %H A351630 Urban Larsson, Simon Rubinstein-Salzedo, and Aaron N. Siegel, <a href="https://arxiv.org/abs/1912.10517">Memgames</a>, arXiv:1912.10517 [math.CO], 2019. %Y A351630 Cf. A131469. %K A351630 nonn,hard,more %O A351630 0,2 %A A351630 _Aaron N. Siegel_, Jun 01 2022