A071080 Determinant of the n X n matrix whose element (i,j) equals the |i-j|-th composite number, or 1 if i=j.

1, -15, 125, -935, 6096, -38340, 240864, -1497584, 8611328, -49201152, 277473280, -1541996288, 7852493824, -39972516864, 195624648704, -789661486080, 3052709008384, -9659706075392, 30089357409792, -63825905935360, 63965499203712, -8296932715920, -1139418909751008

Offset: 1

Author

Robert G. Wilson v, May 26 2002

Keywords

• sign

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A071078, A071079, A071081, A071082, A071083.

Cf. A374069 (permanent).

Programs

Maple

comps:= remove(isprime,[$4 .. 1000]):
f:= proc(n) local M;
  M:= Matrix(n,n,(i,j) -> `if`(i=j,1,comps[abs(i-j)]));
  LinearAlgebra:-Determinant(M)
end proc:
map(f, [$1..25]); # Robert Israel, Dec 03 2024

Mathematica

Composite[n_Integer] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; f[n_] := Det[ Table[ If[i == j, 1, Composite[ Abs[i - j]]], {i, 1, n}, {j, 1, n}]]; Table[ f[n], {n, 1, 20}]

Extensions

a(21)-a(23) from Stefano Spezia, Jun 27 2024