Nim Sequence Calculation

In 1988, using Elwyn Berlekamp's "Sparse Spaces and Common Cosets" algorithm, Anil Gangolli and I calculated that the octal game .16 has a periodic nim sequence of length 149459 (a prime number) after an initial preperiod of length 105351. We also discovered the periods of length 144, 4, and 4 for the octal games .56, .127, and .376, respectively.

Here's an archived abstract of a talk I gave at Stanford.

Since then others have applied more powerful computers and the sparse space and common coset algorithm to find even longer octal game nim sequence periods.

Achim Flammenkamp in particular has verified and extended these results, collecting together previous results of Richard K. Guy, C. A. B. Smith, Jack Kenyon, and others with lots of more recent computation that he has done.

For example, Flammenkamp discovered that .106 has a period of length

328226140474
with initial preperiod of length

465384263797.