A228638 Determinant of the n X n matrix with (i,j)-entry equal to 1 or 0 according as |i-j| is prime or not.

0, 0, 0, 1, 2, -5, 12, -28, 32, -36, -44, -51, 90, -129, -572, 560, -228, -1265, -3752, -7344, -7168, -5200, -1800, 22225, -223908, -3353049, -16485870, -46205099, 57203700, 262750475, -1758254750, -4839494944, -8039222088, 8145218368, 45619374914, -1229448140891, -1178481640872, -942903100573, 1256162791268, -805110454771

Offset: 1

Author

Zhi-Wei Sun, Aug 28 2013

Keywords

• sign

Comments

Conjecture: a(n) is nonzero for any n > 3.

Examples

			a(1) = 0 since |1-1| = 0 is not a prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A228626, A228615, A228616, A228623, A228624.

Programs

Mathematica

a[n_]:=Det[Table[If[PrimeQ[Abs[i-j]]==True,1,0],{i,1,n},{j,1,n}]]
Table[a[n],{n,1,50}]