Octal games

[Richard Guy]

I don't know when, during the last 50 years,
that this mistake crept in!  It's amazing that
no-one has pointed it out earlier.  The
nim-values for the two games are given correctly
(I believe?) in the 1956 (but written in the
late forties) Proc Camb Phil Soc paper with 
Cedric Smith, except that we omitted the
exception  G(31) = 2  in Dawson's Kayles (of
which .07 is first cousin) on p.517.  The rule
is certainly wrong for (all sufficiently large)
n  congruent to  1, 15, 17, 18  mod 34.    R.

On Tue, 22 Oct 2002, Christian G. Bower wrote:

> In _Winning Ways_ pg. 93 (2nd edition, Vol 1) a comparison is made between
> the octal games .17 and .07 showing them to be the same at even n and
> differ by a Nim addition of 1 at odd n.
> 
> However, I calculated several values of the two games and found some
> discrepancies to that rule.
> 
> The first at n=49, both games giving a value of 4.
> The next at n=51, .17 giving 7 and .07 giving 5.
> 
> The next ones at: 69 83 85 86 103 117 119 120 137 151 153 154 171 185
> 187 188
> 
> These values agree with the values Joseph Myers calculated in the EIS
> sequence A071431.
> 
> Also in Table 6 the code "x" is listed as 1,2,3. It appears it should be
> 0,1,2,3.
> 
> Christian
> 
> 
>