A071079 Determinant of the n X n matrix whose element (i,j) equals the |i-j|-th prime or if i=j, 0.

1, 0, -4, 24, -135, 696, -3577, 8738, -21120, 7182, 85995, 307692, -4739379, 72588316, 1042545852, 13023653868, -40433805531, -160245671048, 2415459163787, 80057252715814, -4733090488738644, 277504161503477090, -7200884073495803561, 97750528494490914120

Offset: 0

Author

Robert G. Wilson v, May 26 2002

Keywords

• sign

Crossrefs

Cf. A071078, A071082, A071083.

Programs

Maple

a:= n-> LinearAlgebra[Determinant](Matrix(n,
   (i, j)-> `if`(i=j, 0, ithprime(abs(i-j))))):
seq(a(n), n=0..24);  # Alois P. Heinz, Jun 27 2024

Mathematica

f[n_] := Det[ Table[ If[ i == j, 0, Prime[ Abs[i - j]]], {i, 1, n}, {j, 1, n}]]; Table[ f[n], {n, 1, 20}]

Extensions

More terms from Sean A. Irvine, Jun 27 2024

a(0)=1 prepended by Alois P. Heinz, Jun 27 2024