Re: Guess the Permutation (spoiler included)

From: Jyrki Lahtonen (lahtonen_at_utu.fi)
Date: 01/14/05 

Date: Fri, 14 Jan 2005 10:24:46 +0200

Leroy Quet wrote:

> a(2n-1) = the lowest positive integer not occurring earlier in the
> sequence.
>
> a(2n) = the a(2n-1)th lowest positive integer not occurring earlier in
> the sequence.
>
Ok!

As I know that you are fascinated by various games I need to
ask you the following: Are the pairs (a(2n-1),a(2n)) the
"goals" in a winning strategy of a game, where you subtract
counters from two piles according to some rules? E.g. the
game of Wythoff leads to such a permutation of N, where
a(2n-1) are determined exactly as in your rule, but the
a(2n) are determined by the rule a(2n)=a(2n-1)+n. The
resulting sequence then has a nice closed form expression
involving powers of phi=(1+sqrt5)/2 and the floor function.

I'll think about your rule (when I can find the time:)

Cheers,

Jyrki

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