%I #56 Sep 23 2024 11:57:29
%S 2,2,2,2,1,2,1,2,2,2,1,2,1,2,2
%N a(n) = 1 if first player in Sylver coinage game can force a win by choosing n as the first number, otherwise a(n) = 2.
%C Although a(16) is not known, a few later terms are known. For example a(17)=1.
%C J. H. Conway offered $1000 for the value (with proof) of a(16).
%H Jared DeLeo, <a href="https://arxiv.org/abs/2409.00268">Uniform Shared Neighborhood Structures in Edge-Regular Graphs</a>, arXiv:2409.00268 [math.CO], 2024. See p. 15.
%H Joshua Fallon, Kirsten Hogenson, Lauren Keough, Mario Lomelí, Marcus Schaefer, and Pablo Soberón, <a href="https://arxiv.org/abs/1808.00385">A Note on the Maximum Rectilinear Crossing Number of Spiders</a>, arXiv:1808.00385 [math.CO], 2018.
%H Aleksandar Jurišić and Janoš Vidali, <a href="https://doi.org/10.22405/2226-8383-2019-20-2-198-206">No strongly regular graph is locally Heawood</a>, Chebyshevskii Sbornik (2020) Vol. 20, No. 2, 199-206.
%H OEIS50 DIMACS Conference on Challenges of Identifying Integer Sequences, <a href="https://vimeo.com/109815595">Problem Session 2, Oct 10 2014</a>, J. H. Conway, Five $1000 Problems (starting at about 06.44). This sequence is mentioned in the first problem.
%H Reimbay Reimbayev, <a href="https://arxiv.org/abs/2409.10620">The Lower Bound for Number of Hexagons in Strongly Regular Graphs with Parameters lambda = 1 and mu = 2</a>, arXiv:2409.10620 [math.CO], 2024. See p. 12.
%H Tal Schuster, Ashwin Kalyan, Oleksandr Polozov, and Adam Tauman Kalai, <a href="https://arxiv.org/abs/2106.05784">Programming Puzzles</a>, arXiv:2106.05784 [cs.LG], 2021.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Sylver_coinage">Sylver coinage</a>
%H Sa’ar Zehavi and Ivo Fagundes David de Oliveira, <a href="https://pdfs.semanticscholar.org/e255/c947033f11fd269f9f9525a7bdfe02a27b77.pdf">Not Conway's 99-Graph Problem</a>, research paper, Department of Computer Science, Technion, Sep 15 2017.
%H Doron Zeilberger, <a href="http://sites.math.rutgers.edu/~zeilberg/oeis50.html">Videos of Talks Delivered in SLOANE75/OEIS50 DIMACS Conference on Challenges of Identifying Integer Sequences</a> (see Problem Session 2, Oct 10 2014)
%K nonn,more,hard
%O 1,1
%A _N. J. A. Sloane_, Oct 10 2014