A340923 4*a(n) is the maximum possible determinant of a 3 X 3 matrix whose entries are 9 consecutive primes starting with prime(n).

1660, 2693, 3894, 5712, 7030, 9155, 10369, 11718, 14480, 16185, 18774, 20070, 22920, 24720, 23895, 26800, 31560, 39117, 43080, 43245, 42132, 38406, 41056, 48204, 66144, 69006, 86556, 98499, 99021, 88999, 77640, 87348, 86745, 89832, 92466, 95277, 98454, 84820

Offset: 1

Author

Hugo Pfoertner, Jan 26 2021

Keywords

• nonn

Comments

The entries of the matrix are arranged in such a way that the determinant of the matrix is maximized.

Examples

			a(1) = 1660 = A180128(3)/4 with the corresponding matrix shown in A180128.
a(2) = 2693: determinant (
  [13 29  7]
  [ 3 11 23]
  [19  5 17]) = 10772 = 4*2693.
		

Crossrefs

Cf. A117330, A180128, A340924, A340925.

Programs

Mathematica

Table[Max[Det[Partition[#,3]]&/@Permutations[Prime[Range[n,n+8]]]],{n,40}]/4 (* Harvey P. Dale, Jul 21 2021 *)