A118875 Determinant of n-th continuous block of 9 consecutive squares of primes.

-213720, 114432, -548352, 892800, -1774080, -7289856, 10105344, -79557120, -97790976, 171740160, 147556224, 56531520, -380053440, 122206464, -164292480, -958000320, 394761600, 189907200, 1139760000, -3023127360, -1495428480, -4260988800, -14501393280, 7022695680

Offset: 1

Author

Jonathan Vos Post, May 24 2006

Keywords

• easy
• sign

Comments

Quadratic analog of A117330 Determinants of 3 X 3 matrices of continuous blocks of 9 consecutive primes. See also: A001248 Squares of primes. The terminology "continuous" is used to distinguish from "discrete" which would be block 1: 4, 9, 25, 49, 121, 169, 289, 361, 529; block 2: 841, 961, 1369, 1681, 1849, 2209, 2809, 3481, 3721; and so forth.

Examples

			a(1) = -213720 =
  |  4    9   25|
  | 49  121  169|
  |289  361  529|.
a(2) =
  |   9  25  49|
  | 121 169 289|
  | 361 529 841|.
		

Crossrefs

Cf. A000040, A001248, A117301, A117330.

Programs

Maple

a:= n-> LinearAlgebra[Determinant](Matrix(3, (i,j)-> ithprime(n+3*i-4+j)^2)):
seq(a(n), n=1..25);  # Alois P. Heinz, Jan 25 2021

Mathematica

m = 24; p = Prime[Range[m + 8]]^2; Table[Det @ Partition[p[[n ;; n + 8]], 3], {n, 1, m}] (* Amiram Eldar, Jan 25 2021 *)

PARI

a(n) = matdet(matrix(3, 3, i, j, prime((n+j-1)+3*(i-1))^2)); \\ Michel Marcus, Jan 25 2021

Extensions

Wrong Formula and data corrected by Michel Marcus, Jan 25 2021