A340925 16*a(n) is the maximum possible determinant of a 5 X 5 matrix whose entries are 25 consecutive primes starting with prime(n).

445934520, 527275650, 606375810, 668638620, 732258072, 860414368, 995563032, 1132837302, 1249798972, 1453587865, 1598993079, 1789976248, 2008319824, 2181193410, 2363922414, 2592209412, 2782039915, 3035727819, 3255326094, 3421333460, 3453338250, 3663999760, 4056944944

Offset

2,1

Comments

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

The special case of the first matrix with determinant A180128(5) = 5725998504 is excluded, since the prime number 2 prevents the otherwise existing divisibility of the determinant by 16.

Links

Table of n, a(n) for n=2..24.

Example

a(2) = 445934520: determinant(
  [73  53  3 79 23]
  [37 101 43  5 47]
  [19  41 89 71 13]
  [11  31 29 61 97]
  [83   7 67 17 59]) = 7134952320 = 16*445934520.

Crossrefs

Cf. A118815, A180128, A340923, A340924.

Sequence in context: A209210 A047989 A342857 * A280001 A096556 A038830

Adjacent sequences: A340922 A340923 A340924 * A340926 A340927 A340928

Keyword

nonn

Author

Hugo Pfoertner, Jan 26 2021

Status

approved