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A066933
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Determinant of n X n matrix whose rows are cyclic permutations of 2..prime(n).
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12
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1, 2, -5, -70, 1275, 97748, -2713585, -251983958, 9651414311, 1137214908700, -268100912462097, -16553358418854560, 4303513869962179379, 602501593820064477686, -50199332236439321779977, -7847812115804566640572424, 2754406130856424049914030863
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OFFSET
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0,2
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LINKS
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FORMULA
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Conjecture: a(n) = (-1)^(n+floor(n/2))*Res(f(n) , x^n - 1), where Res is the resultant, and f(n)=Sum_{k=1..n} prime(k)*x^k. - Benedict W. J. Irwin, Dec 07 2016
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EXAMPLE
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a(3) = -70 because this is the determinant of [(2,3,5), (3,5,2), (5,2,3)].
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MAPLE
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a:= n-> LinearAlgebra[Determinant](Matrix(n,
(i, j)-> ithprime(1+irem(i+j-2, n)))):
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MATHEMATICA
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f[ n_ ] := Module[ {a = Table[ Prime[ i ], {i, 1, n} ], m = {}, k = 0}, While[ k < n, m = Append[ m, RotateLeft[ a, k ] ]; k++ ]; Det[ m ] ]; Table[ f[ n ], {n, 1, 16} ]
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PROG
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(PARI) a(n) = matdet(matrix(n, n, i, j, prime(1+lift(Mod(i+j-2, n))))); \\ Michel Marcus, Aug 11 2019; corrected Jun 12 2022
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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