[seqfan] Re: Prime Sums In A Grid

[Leroy Quet]

If you are too lazy to check the link, this "game" can be easily summerized here.

Write the integers 1 through n^2 into the squares of an n-by-n grid, one number per square.

For an n-by-n grid, what is the maximum possible number of "pairs" of integers that each sum to a prime, where a "pair" is any two numbers that are immediately adjacent in the grid in the direction of either up, down, left, or right?

Thanks,
Leroy Quet


--- On Sun, 2/22/09, Leroy Quet <q1qq2qqq3qqqq at yahoo.com> wrote:

> Consider the game here:
> 
> http://gamesconceived.blogspot.com/2008/09/prime-sum-game.html
> 
> How does the sequence {a(k)} begin, where a(n) = the
> highest possible 1-player score for an n-by-n grid? (Or a(n)
> = the highest possible sum of the scores of all players
> playing on an n-by-n grid, as far as multi-player games go.)
> 
> I get (with the first term being a(1)) the sequence
> beginning:
> 
> 0,4,11,...
> 
> An example of a 3-by-3 grid with 11 prime sums is:
> 
> 5 2 3
> 6 1 8
> 7 4 9
> 
> (Only the pair of adjacent numbers (1,8) sum to a
> composite.)
> 
> Thanks,
> Leroy Quet
> 
> PS: I am posting this to sci.math as well.
> 
> 
> 
> 
> 
>       
> 
> 
> 
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