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A024356 Determinant of Hankel matrix of the first 2n-1 prime numbers. 5
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; text; internal format)
OFFSET

0,2

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, Mar 22 2004

LINKS

K. Brockhaus, Table of n, a(n) for n = 0..200 [From Klaus Brockhaus, May 12 2010]

EXAMPLE

a(2) = 1 because det[[2,3],[3,5]] = 1

From Klaus Brockhaus, 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)

PROG

(PARI) for (i=0, 20, print1(", "matdet(matrix(i, i, X, Y, prime(X+Y-1))))) (Perry)

From Klaus Brockhaus, 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)

CROSSREFS

Cf. A290302.

Sequence in context: A121310 A278158 A218880 * A143947 A226518 A073781

Adjacent sequences:  A024353 A024354 A024355 * A024357 A024358 A024359

KEYWORD

sign

AUTHOR

Jeffrey Shallit, Jun 08 2000

STATUS

approved

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Last modified February 23 04:21 EST 2019. Contains 320411 sequences. (Running on oeis4.)