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A228623
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Determinant of the n X n matrix with (i,j)-entry (i,j = 0,...,n-1) equal to 1 or 0 according as n + i - j and n - i + j are both prime or not.
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3
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0, 1, 1, 1, 0, -1, 0, 0, 0, -4, -1, 0, 0, 0, -6, 0, 0, -144, 0, 0, 0, -1, 168, 1024, 420, 0, 0, 0, -1, -9801, 0, 144, 0, 0, 3072, 7056, 0, 0, -42346434, 0, 0, -331776, 0, 0, 36528128, -104976, 96545145, 0, 34665386, -62500, 2826240, 2025, 0, -23174596, 0, 0, 255578880, -4, -3, 990172089
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OFFSET
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1,10
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COMMENTS
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Conjecture: a(n) is nonzero if n is odd and greater than 120.
This implies Goldbach's conjecture for even numbers of the form 4*k + 2.
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LINKS
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EXAMPLE
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a(1) = 0 since 1 + 0 - 0 = 1 is not a prime.
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MATHEMATICA
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a[n_]:=Det[Table[If[PrimeQ[n+j-i]==True&&PrimeQ[n+i-j]==True, 1, 0], {i, 0, n-1}, {j, 0, n-1}]]
Table[a[n], {n, 1, 20}]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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