

A117330


a(n) is the determinant of the 3 X 3 matrix with entries the 9 consecutive primes starting with the nth 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
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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+j1)+3*(i1)))); \\ 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



