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

1,1

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.

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A278654 A331630 A098024 * A033398 A204376 A176094

Adjacent sequences: A117327 A117328 A117329 * A117331 A117332 A117333

Keyword

easy,sign

Author

Cino Hilliard and Walter Kehowski, Apr 24 2006

Extensions

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

Status

approved