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A117330
a(n) is the determinant of the 3 X 3 matrix with entries the 9 consecutive primes starting with the n-th prime.
11
-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
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
KEYWORD
easy,sign
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane at the suggestion of Stefan Steinerberger, Jul 14 2007
STATUS
approved