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

Author

Cino Hilliard and Walter Kehowski, Apr 24 2006

Keywords

• easy
• sign

Comments

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.

Examples

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

Links

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

Crossrefs

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

Programs

Maple

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

Mathematica

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

PARI

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

Formula

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

Extensions

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