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Search: id:A118983
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| A118983 |
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Determinant of 3 X 3 matrices of n-th continuous block of 9 consecutive composites. |
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+0
1
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| 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
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OFFSET
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1,1
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COMMENT
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Composites analogue of A117330 Determinants of 3 X 3 matrices of continuous blocks of 9 consecutive primes. See also: A118781 Determinants of 3 X 3 matrices of continuous blocks of 9 consecutive semiprimes. The terminology "continuous" is used to distinguish from "discrete" which would be (in this composites case) block 1: 4, 6, 8, 9, 10, 12, 14, 15, 16; block 2: 18, 20, 21, 22, 24, 25, 26, 27, 28; and so forth. a(30) = 50 has 50 as the central element of its matrix. a(32) = 7 is the first prime value in the sequence.
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FORMULA
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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.
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EXAMPLE
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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|.
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CROSSREFS
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Cf. A002808, A117301, A117330, A118780, A118781.
Adjacent sequences: A118980 A118981 A118982 this_sequence A118984 A118985 A118986
Sequence in context: A040557 A040556 A070663 this_sequence A033968 A033344 A079341
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KEYWORD
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easy,sign,less
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), May 25 2006
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