A118815 -id:A118815 - cp's OEIS frontend

A117330 a(n) is the determinant of the 3 X 3 matrix with entries the 9 consecutive primes starting with the n-th prime.

-78, 20, -36, 36, -40, -96, 96, -480, -424, 520, 348, 100, -540, 144, -144, -712, 240, 96, 480, -1120, -468, -1152, -3384, 1404, -576, -3924, 7884, -1548, -7312, 6288, -1828, -528, -768, 1920, 720, 768, -1920, 2400, -944, -9340, 12588, 15540, -864, 5600, 4124, -13668, -1428, 1552

Offset: 1

Cino Hilliard and Walter Kehowski, Apr 24 2006

The first term -78 is 6 mod 12 but all subsequent terms are 0,4,8 mod 12. Checked out to n=10000. A117329 is the subsequence formed by taking every 9th term.

The smallest absolute value of the sequence is 0.

			a(3)=-36 = det([[5,7,11],[13,17,19],[23,29,31]]).

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

Cf. A117329, A117345, A118799, A118815, A340869.

primedet := proc(n) local L; L:=map(ithprime,[$n..n+8]); linalg[det]([L[1..3],L[4..6],L[7..9]]) end;

Table[Det[Partition[Prime[Range[n,n+8]],3,3]],{n,50}] (* Harvey P. Dale, May 16 2019 *)

a(n) = matdet(matrix(3,3,i,j,prime((n+j-1)+3*(i-1)))); \\ Michel Marcus, Jan 25 2021

a(A117345(n)) = 0. - Hugo Pfoertner, Jan 26 2021

Edited by N. J. A. Sloane at the suggestion of Stefan Steinerberger, Jul 14 2007

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).

Original entry on oeis.org

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

Hugo Pfoertner, Jan 26 2021

nonn

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.

			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.

Cf. A118815, A180128, A340923, A340924.

cp's OEIS Frontend

A117330 a(n) is the determinant of the 3 X 3 matrix with entries the 9 consecutive primes starting with the n-th prime.

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