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%I #29 Jan 26 2021 10:23:06
%S -78,20,-36,36,-40,-96,96,-480,-424,520,348,100,-540,144,-144,-712,
%T 240,96,480,-1120,-468,-1152,-3384,1404,-576,-3924,7884,-1548,-7312,
%U 6288,-1828,-528,-768,1920,720,768,-1920,2400,-944,-9340,12588,15540,-864,5600,4124,-13668,-1428,1552
%N a(n) is the determinant of the 3 X 3 matrix with entries the 9 consecutive primes starting with the n-th prime.
%C 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.
%C The smallest absolute value of the sequence is 0.
%H Harvey P. Dale, <a href="/A117330/b117330.txt">Table of n, a(n) for n = 1..1000</a>
%F a(A117345(n)) = 0. - _Hugo Pfoertner_, Jan 26 2021
%e a(3)=-36 = det([[5,7,11],[13,17,19],[23,29,31]]).
%p primedet := proc(n) local L; L:=map(ithprime,[$n..n+8]); linalg[det]([L[1..3],L[4..6],L[7..9]]) end;
%t Table[Det[Partition[Prime[Range[n,n+8]],3,3]],{n,50}] (* _Harvey P. Dale_, May 16 2019 *)
%o (PARI) a(n) = matdet(matrix(3,3,i,j,prime((n+j-1)+3*(i-1)))); \\ _Michel Marcus_, Jan 25 2021
%Y Cf. A117329, A117345, A118799, A118815, A340869.
%K easy,sign
%O 1,1
%A _Cino Hilliard_ and _Walter Kehowski_, Apr 24 2006
%E Edited by _N. J. A. Sloane_ at the suggestion of _Stefan Steinerberger_, Jul 14 2007