A006018 List of periods for game of Third One Lucky. (Formerly M0932)

1, 2, 4, 2, 12, 12, 12, 8, 8, 10, 60, 60, 84, 84, 84, 16, 16, 18, 180, 20, 900, 7200, 7200, 24, 24, 26, 364, 364, 2184

Offset

1,2

Comments

From Aidan Hennessey, Apr 27 2024: (Start)

Third One Lucky is equivalent to Tripod Nim with 2 in the center. More values have been calculated than are listed, but there are gaps.

It is known that every term after the first is even. (End)

References

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 487.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..29.

Aidan Hennessey, Tree and Tripod Nim, arXiv:2401.07943 [math.CO], 2024. Mentions this sequence.

Formula

Conjectures from Aidan Hennessey, Apr 27 2024: (Start)

Temporarily setting b(n) = a(n+1), i.e. if the offset were 0, then:

b(8k-1) divides 8k for k>0.

For each k>0 either:

1) b(8k) divides 8k, b(8k+1) divides 8k+2, b(8k+2) and b(8k+3) divide 2(4k+1)(4k+2) OR

2) b(8k) and b(8k+1) divide 8k(4k+1). (End)

Crossrefs

Sequence in context: A181091 A161795 A138770 * A152666 A153801 A354408

Adjacent sequences: A006015 A006016 A006017 * A006019 A006020 A006021

Keyword

hard,nonn,more

Author

N. J. A. Sloane

Extensions

Inserted 16 between the current 16th and 17th entry. This is an error in Winning Ways. I thank Emilie Hogan, my graduate student, for pointing this out. - Doron Zeilberger, Dec 09 2008

Terms 900, 7200, 7200, 24, 24, 26, 364, 364, 2184 added by Aidan Hennessey, Apr 27 2024

Status

approved