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 A118983 Determinant of 3 X 3 matrices of n-th continuous block of 9 consecutive composites. 1
 24, 12, 0, 15, 30, 18, -4, -4, 34, -4, -4, 22, 8, 8, 0, -8, -8, 38, 4, 4, 26, 4, 4, 42, -4, -4, 58, -4, -4, 50, 4, 7, -7, -4, 52, 8, 8, 0, -8, -8, 68, 4, 4, 56, 4, 4, 80, -8, -8, 80, 4, 4, -4, 0, 4, -4, -4, 86, 4, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Analog of A117330 with composites instead of primes. LINKS Table of n, a(n) for n=1..60. FORMULA a(n) = c(n)*c(n+4)*c(n+8) - c(n)*c(n+5)*c(n+7) - c(n+1)*c(n+3)*c(n+8) + c(n+1)*c(n+5)*c(n+6) + c(n+2)*c(n+3)*c(n+7) - c(n+2)*c(n+4)*c(n+6) where c(n) = A002808(n) is the n-th composite. EXAMPLE a(1) = 24 = | 4 6 8| | 9 10 12| |14 15 16|. a(3) = 0 because of the first of an infinite number of singular matrices: | 8 9 10| |12 14 15| |16 18 20|. a(15) = 0 because of the singular matrix: |25 26 27| |28 30 32| |33 34 35|. a(38) = 0 because of the singular matrix: |55 56 57| |58 60 62| |63 64 65|. a(54) = 0 because of the singular matrix: |76 77 78| |80 81 82| |84 85 86|. MAPLE A118983 := proc(n) A002808(n)*A002808(n+4)*A002808(n+8) -A002808(n)*A002808(n+5) *A002808(n+7) -A002808(n+1)*A002808(n+3) *A002808(n+8) +A002808(n+1)*A002808(n+5) *A002808(n+6) +A002808(n+2)*A002808(n+3) *A002808(n+7) -A002808(n+2)*A002808(n+4) *A002808(n+6) ; end proc: seq(A118983(n), n=1..60) ; # R. J. Mathar, Dec 22 2010 MATHEMATICA Det[#]&/@(Partition[#, 3]&/@Partition[Select[Range[100], CompositeQ], 9, 1]) (* Harvey P. Dale, May 16 2019 *) PROG (PARI) c(n) = for(k=0, primepi(n), isprime(n++)&&k--); n; \\ A002808 a(n) = matdet(matrix(3, 3, i, j, c((n+j-1)+3*(i-1)))); \\ Michel Marcus, Jan 25 2021 CROSSREFS Cf. A002808, A117301, A117330, A118780, A118781. Sequence in context: A343389 A267024 A259337 * A033968 A033344 A228437 Adjacent sequences: A118980 A118981 A118982 * A118984 A118985 A118986 KEYWORD easy,sign,less AUTHOR Jonathan Vos Post, May 25 2006 STATUS approved

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Last modified June 17 03:24 EDT 2024. Contains 373432 sequences. (Running on oeis4.)