A071082 Determinant of the n X n matrix whose element (i,j) equals the (i-j)-th composite number, (j-i)-th prime number, or 1 if i=j.

1, -7, 39, -231, 1175, -6404, 34516, -194372, 914065, -4380707, 19511875, -48269825, 364029100, -2195115952, 13627012744, -115725814173, 792363218461, -5961225064275, 50261904138348, -425928565835370, 3704468293623774, -34926740161083290, 389473974875205556

Offset: 1

Author

Robert G. Wilson v, May 26 2002

Keywords

• sign

Crossrefs

Cf. A071078, A071079.

Programs

Mathematica

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

Extensions

More terms from Sean A. Irvine, Jun 27 2024