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 A374910 #20 Aug 08 2024 12:42:36
%S A374910 1,25,26,31,32,37,38,63,64,69,70,76,101,102,139,145,177,189,215,235,
%T A374910 252,253,267,284,290,305,311,328,360,668
%N A374910 Values k such that the two-player impartial {0,1}-Toggle game on a path P(k+4) = v(1)v(2)...v(k+4) with a (1^k,0,1,0,1)-weight assignment is a second-player winning game.
%C A374910 The two-player impartial {0,1}-Toggle game is played on a simple connected graph G where each vertex is assigned an initial weight of 0 or 1.
%C A374910 A Toggle move consists of selecting a vertex v and switching its weight as well as the weight of each of its neighbors. This move is only legal provided the weight of vertex v is 1 and the total sum of the vertex weights decreases.
%C A374910 In the special case G=P(k+4), a (1^k,0,1,0,1)-weight assignment is one in which vertices v(k+1) and v(k+3) are assigned weight 0 and all remaining vertices are assigned weight 1.
%C A374910 The path P(k+4m) where vertices v(k+1), v(k+3), ..., v(k+4m-1) are assigned weight 0 and all remaining vertices are assigned weight 1 will have the same Grundy numbers as G.
%D A374910 E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays, Vol. 1, CRC Press, 2001.
%H A374910 K. Barker, M. DeStefano, E. Fiorini, M. Gohn, J. Miller, J. Roeder, and T. W. H. Wong, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL27/Wong/wong43.html">Generalized Impartial Two-player Pebbling Games on K3 and C4</a>, Journal of Integer Sequences, 27(5), 2024.
%H A374910 Matthew Cohen, <a href="/A374910/a374910.py.txt">Python</a>
%H A374910 E. Fiorini, M. Lind, A. Woldar, and T. W. H. Wong, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL24/Wong/wong31.pdf">Characterizing Winning Positions in the Impartial Two-Player Pebbling Game on Complete Graphs</a>, Journal of Integer Sequences, 24(6), 2021.
%o A374910 (Python) # See Cohen link.
%Y A374910 Cf. A071426, A340631, A346197, A346401, A346637, A361517, A374810, A374920.
%K A374910 nonn,more
%O A374910 1,2
%A A374910 _Patrick G. Cesarz_, _Matthew Cohen_, _Eugene Fiorini_, _Joshua Lowrance_, _Emily Riley_, _Angel Pedro Torres_ and _Andrew Woldar_, Jul 20 2024