A248380 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.

2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2

Offset

1,1

Comments

Although a(16) is not known, a few later terms are known. For example a(17)=1.

J. H. Conway offered $1000 for the value (with proof) of a(16).

Links

Table of n, a(n) for n=1..15.

Jared DeLeo, Uniform Shared Neighborhood Structures in Edge-Regular Graphs, arXiv:2409.00268 [math.CO], 2024. See p. 15.

Joshua Fallon, Kirsten Hogenson, Lauren Keough, Mario Lomelí, Marcus Schaefer, and Pablo Soberón, A Note on the Maximum Rectilinear Crossing Number of Spiders, arXiv:1808.00385 [math.CO], 2018.

Aleksandar Jurišić and Janoš Vidali, No strongly regular graph is locally Heawood, Chebyshevskii Sbornik (2020) Vol. 20, No. 2, 199-206.

OEIS50 DIMACS Conference on Challenges of Identifying Integer Sequences, Problem Session 2, Oct 10 2014, J. H. Conway, Five $1000 Problems (starting at about 06.44). This sequence is mentioned in the first problem.

Reimbay Reimbayev, The Lower Bound for Number of Hexagons in Strongly Regular Graphs with Parameters lambda = 1 and mu = 2, arXiv:2409.10620 [math.CO], 2024. See p. 12.

Tal Schuster, Ashwin Kalyan, Oleksandr Polozov, and Adam Tauman Kalai, Programming Puzzles, arXiv:2106.05784 [cs.LG], 2021.

Wikipedia, Sylver coinage

Sa’ar Zehavi and Ivo Fagundes David de Oliveira, Not Conway's 99-Graph Problem, research paper, Department of Computer Science, Technion, Sep 15 2017.

Doron Zeilberger, Videos of Talks Delivered in SLOANE75/OEIS50 DIMACS Conference on Challenges of Identifying Integer Sequences (see Problem Session 2, Oct 10 2014)

Crossrefs

Sequence in context: A236472 A175357 A232800 * A090044 A036238 A318723

Adjacent sequences: A248377 A248378 A248379 * A248381 A248382 A248383

Keyword

nonn,more,hard

Author

N. J. A. Sloane, Oct 10 2014

Status

approved