A118799 Determinants of 4 X 4 matrices of 16 consecutive primes.

880, -448, -1472, -240, 2480, -1352, -4128, -96, 2736, -2520, 120, 1080, 4288, 4880, 4600, 13368, 7056, 14560, 2960, 13320, 0, 24864, -11096, -24264, 0, -9168, -2128, -15792, 0, 18120, -5248, 6384, -21840, -38776, -20480, 20176, -72896, -69200, 40080, -37632

Offset: 1

Author

Jonathan Vos Post, May 23 2006

Keywords

• easy
• sign

Comments

4 X 4 analog of A117330.

All terms are even. - Harvey P. Dale, May 05 2016

Examples

			a(1) = 880 =
  | 2  3  5  7|
  |11 13 17 19|
  |23 29 31 37|
  |41 43 47 53|.
a(10) = -2520 =
  |29 31 37 41|
  |43 47 53 59|
  |61 67 71 73|
  |79 83 89 97|.
a(21) = 0 =
  | 73  79  83  89|
  | 97 101 103 107|
  |109 113 127 131|
  |137 139 149 151|.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A067276, A117301, A117330 , A118713.

Programs

Maple

A118799 := proc(n)
    local A,i,r,c ;
    A := Matrix(4,4) ;
    i := n ;
    for r from 1 to 4 do
    for c from 1 to 4 do
        A[r,c] := ithprime(i) ;
        i := i+1 ;
    end do:
    end do:
    LinearAlgebra[Determinant](A) ;
end proc: # R. J. Mathar, May 05 2013

Mathematica

Module[{nn=60,prs},prs=Prime[Range[nn]];Table[Det[Partition[ Take[ prs, {n,n+15}],4]],{n,nn-15}]] (* Harvey P. Dale, Apr 29 2016 *)

PARI

a(n) = matdet(matrix(4,4,i,j,prime((n+j-1)+4*(i-1)))); \\ Michel Marcus, Jan 25 2021