A024356 Determinant of Hankel matrix of the first 2n-1 prime numbers.

1, 2, 1, -2, 0, 288, -1728, -26240, 222272, 1636864, -8434688, -61820416, 238704640, 544024576, 3294658560, -71814283264, 359994671104, 17294535000064, 302441193013248, -2311203985948672, -11313883306262528, -31078379553816576, 26574426771056230400

Offset: 0

Author

Jeffrey Shallit, Jun 08 2000

Keywords

• sign

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

Examples

			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)
		

Links

• Klaus Brockhaus, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A290302.

Programs

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] ]; // Klaus Brockhaus, May 12 2010

Mathematica

a[n_]:=Det[Table[Prime[i+j-1],{i,n},{j,n}]]; Join[{1},Array[a, 20]] (* Stefano Spezia, Feb 03 2024 *)

PARI

for (i=0,20,print1(","matdet(matrix(i,i,X,Y,prime(X+Y-1))))) \\ Jon Perry, Mar 22 2004