determinant of a curious class of (0,1) matrices

[Marc LeBrun]

After making a few quick experiments I believe it to be true because it 
appears to be true of any {0,1} matrix for which m(i,j)=0 when i+j is 
odd.  Perhaps this weaker condition would be easier to prove.


At 12:04 PM 4/20/2002 +0200, spados at katamail.com wrote:
>What can you say about the conjecture below?
>
> >%I A000001
> >%S A000001 1, -1, -1, 0, 1, -1, -4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, -9, 
> -25, 121, 64, \
> >-576, -2304, 3600, 3136, -256, -144, 961, 24025, -47089, -345744, 1317904, \
> >107584, -26896, -30976, 17424, 30976, -156025, -76729, 485809, 478864, \
> >-36481, -837225, 5776, 517198564, -15791440896, -16404230241, 45746793225, \
> >54331641, -29465095716
> >%N A000001 a(n) is the determinant of the nXn matrix definided by 
> m(i,j)=1 if i+j
>is a prime m(i,j)=0 otherwise.
> >%C A000001 Conjecture: Abs(a(n)) is always a perfect square.
> >%O A000001 1
> >%K A000001 ,sign,
> >%A A000001 Santi Spadaro (spados at katamail.com), Apr 19 2002
> >RH
>
>Cheers,
>Santi
>
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