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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
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
Sequence in context: A343389 A267024 A259337 * A033968 A033344 A228437
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.)