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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 21 11:09 EDT 2021. Contains 347597 sequences. (Running on oeis4.)