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%I #5 Aug 28 2013 03:02:33
%S 1,0,-1,-2,0,0,0,-2,3,11,24,-60,-16,31,-217,-1148,-164,132,395,697,
%T -191,-76,125664,-213885,-171654,114902,353497,-388325,-1738118,
%U -222898,248633,382075,-1637075,21100,4049068,-189147708,-279083383,472023163,-19063401,-6718578823
%N Determinant of the n X n matrix with (i,j)-entry equal to 1 or 0 according as 2*(i + j) - 1 is prime or not.
%C Conjecture: a(n) is nonzero for any n > 7.
%C Clearly this conjecture implies that there are infinitely many primes.
%H Zhi-Wei Sun, <a href="/A228616/b228616.txt">Table of n, a(n) for n = 1..250</a>
%e a(1) = 1 since 2*(1 + 1) - 1 = 3 is a prime.
%t a[n_]:=a[n]=Det[Table[If[PrimeQ[2(i+j)-1],1,0],{i,1,n},{j,1,n}]]
%t Table[a[n],{n,1,40}]
%Y Cf. A000040, A069191, A228615, A228591.
%K sign
%O 1,4
%A _Zhi-Wei Sun_, Aug 27 2013
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