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A118799
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Determinants of 4 X 4 matrices of continuous blocks of 16 consecutive primes.
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3
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880, -448, -1472, -240, 2480, -1352, -4128, -96, 2736, -2520, 120, 1080, 4288, 4880, 4600, 13368, 7056, 14560, 2960, 13320, 0, 24864, -11096, -24264, 0, -9168, -2128, -15792, 0, 18120, -5248, 6384, -21840, -38776, -20480, 20176, -72896, -69200, 40080, -37632
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OFFSET
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1,1
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COMMENTS
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4 X 4 analogue of A117330 Determinants of 3 X 3 matrices of continuous blocks of 9 consecutive primes. The terminology "continuous" is used to distinguish from "discrete" which would be (in this 4 X 4 prime case) block 1: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53; block 2: 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131; and so forth.
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LINKS
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Table of n, a(n) for n=1..40.
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EXAMPLE
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a(1) = 880 because the determinant of the first continuous block of 16 primes is:
| 2. 3. 5. 7.|
|11. 13. 17. 19.|
|23. 29. 31. 37.|
|41. 43. 47. 53.|.
a(10) = -2520 because the determinant of the 10th continuous block of 16 primes is:
|29. 31. 37. 41.|
|43. 47. 53. 59.|
|61. 67. 71. 73.|
|79. 83. 89. 97.|.
a(21) = 0 because of the singular matrix:
| 73. 79. 83. 89.|
| 97. 101. 103. 107.|
|109. 113. 127. 131.|
|137. 139. 149. 151.|.
a(25) = 0 because of the singular matrix:
| 97. 101. 103. 107.|
|109. 113. 127. 131.|
|137. 139. 149. 151.|
|157. 163. 167. 173.|
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MAPLE
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A118799 := proc(n)
local A, i, r, c ;
A := Matrix(4, 4) ;
i := n ;
for r from 1 to 4 do
for c from 1 to 4 do
A[r, c] := ithprime(i) ;
i := i+1 ;
end do:
end do:
LinearAlgebra[Determinant](A) ;
end proc: # R. J. Mathar, May 05 2013
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CROSSREFS
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Cf. A000040, A067276, A117301, A118713.
Sequence in context: A129313 A063051 A190030 * A206341 A024393 A006052
Adjacent sequences: A118796 A118797 A118798 * A118800 A118801 A118802
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KEYWORD
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easy,sign
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AUTHOR
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Jonathan Vos Post, May 23 2006
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STATUS
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approved
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