A067549 Determinant of n X n matrix whose diagonal are the first n primes and all other elements are 1's.

2, 5, 22, 140, 1448, 17856, 291456, 5338368, 119102976, 3371378688, 102163230720, 3708532408320, 149444916019200, 6320831260262400, 292612319045222400, 15301128319716556800, 891900404470539878400, 53771252059997208576000, 3564336303465704718336000

Offset

1,1

Links

Iain Fox, Table of n, a(n) for n = 1..300

Example

The matrix begins:
  2  1  1  1  1  1  1 ...
  1  3  1  1  1  1  1 ...
  1  1  5  1  1  1  1 ...
  1  1  1  7  1  1  1 ...
  1  1  1  1 11  1  1 ...
  1  1  1  1  1 13  1 ...

Maple

d:=(i, j)->`if`(i<>j, 1, ithprime(i)):
seq(LinearAlgebra[Determinant](Matrix(n, d)), n=1..20); # Muniru A Asiru, Feb 16 2018

Mathematica

Table[ Det[ DiagonalMatrix[ Table[ Prime[ i ] - 1, {i, 1, n} ] ] + 1 ], {n, 1, 20} ]

Prog

(PARI) a(n) = matdet(matrix(n, n, i, j, if(i == j, prime(i), 1))) \\ Iain Fox, Feb 15 2018

Crossrefs

Sequence in context: A342432 A246542 A001437 * A262842 A361331 A342967

Adjacent sequences: A067546 A067547 A067548 * A067550 A067551 A067552

Keyword

nonn

Author

Robert G. Wilson v, Jan 28 2002

Extensions

a(18)-a(19) from Iain Fox, Feb 15 2018

Status

approved