%I #3 Mar 30 2012 17:31:18

%S 1,0,0,1,0,0,0,1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0,0,0,1,1,1,1,1,1,1,

%T 0,1,0,1,0,1,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,0,0,1,1,1,1,1,1,1,

%U 1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0,0,0,0,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0,1

%N Consider the sign of A067276: determinant of n X n matrix containing the first n^2 primes in increasing order; then a(n) = 0 if negative and 1 if positive.

%C The determinant of A can never be 0 since there is an even prime in the mix.

%C Conjecture: This sequence never cycles.

%C Positions where the race between the zeros and the ones is tied: 2,4,16,34,36,38,40,42,46,66,78,80,82,84, ...,.

%t f[n_] := Sign@ Det@ Partition[ Array[Prime, n^2], n]; Array[f, 105] /. -1 -> 0

%Y Cf. A000040, A067276.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, May 26 2006