A228616 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.

1, 0, -1, -2, 0, 0, 0, -2, 3, 11, 24, -60, -16, 31, -217, -1148, -164, 132, 395, 697, -191, -76, 125664, -213885, -171654, 114902, 353497, -388325, -1738118, -222898, 248633, 382075, -1637075, 21100, 4049068, -189147708, -279083383, 472023163, -19063401, -6718578823

Offset: 1

Author

Zhi-Wei Sun, Aug 27 2013

Keywords

• sign

Comments

Conjecture: a(n) is nonzero for any n > 7.

Clearly this conjecture implies that there are infinitely many primes.

Examples

			 a(1) = 1 since 2*(1 + 1) - 1 = 3 is a prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..250

Crossrefs

Cf. A000040, A069191, A228615, A228591.

Programs

Mathematica

a[n_]:=a[n]=Det[Table[If[PrimeQ[2(i+j)-1],1,0],{i,1,n},{j,1,n}]]
Table[a[n],{n,1,40}]