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A024356
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Determinant of Hankel matrix of the first 2n-1 prime numbers.
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4
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1, 2, 1, -2, 0, 288, -1728, -26240, 222272, 1636864, -8434688, -61820416, 238704640, 544024576, 3294658560, -71814283264, 359994671104, 17294535000064, 302441193013248, -2311203985948672, -11313883306262528
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Determinant of n X n matrix with entries prime(X+Y-1).
a(0) = 1 by convention.
I conjecture that a(4) is the only zero. - Jon Perry (perry(AT)globalnet.co.uk), Mar 22 2004
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LINKS
| K. Brockhaus, Table of n, a(n) for n = 0..200 [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 12 2010]
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EXAMPLE
| a(2) = 1 because det[[2,3],[3,5]] = 1
Contribution from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 12 2010: (Start)
a(5) = determinant(M) = 288 where M is the matrix
[ 2 3 5 7 11]
[ 3 5 7 11 13]
[ 5 7 11 13 17]
[ 7 11 13 17 19]
[11 13 17 19 23] (End)
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PROG
| (PARI) for (i=0, 20, print1(", "matdet(matrix(i, i, X, Y, prime(X+Y-1))))) (Perry)
Contribution from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 12 2010: (Start)
(MAGMA) Hankel_prime:=function(n); M:=ScalarMatrix(n, 0); for j in [1..n] do for k in [1..n] do M[j, k]:=NthPrime(j+k-1); end for; end for; return M; end function; [ Determinant(Hankel_prime(n)): n in [0..22] ];
[1] cat [ Determinant( SymmetricMatrix( &cat[ [ NthPrime(j+k-1): k in [1..j] ]: j in [1..n] ] ) ): n in [1..22] ]; (End)
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CROSSREFS
| Sequence in context: A055135 A197522 A121310 * A143947 A073781 A048622
Adjacent sequences: A024353 A024354 A024355 * A024357 A024358 A024359
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KEYWORD
| sign
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AUTHOR
| Jeffrey Shallit (shallit(AT)graceland.uwaterloo.ca), Jun 08 2000
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