A118873 Determinant of n-th continuous block of 4 consecutive squares of primes.

-29, -136, -1704, -6288, -5160, -14928, 52080, -97968, -84000, 98112, -524400, -84048, 637488, 231288, -1558440, -343200, 844152, -2799840, 1152360, 1469160, -783240, 4153800, -4254000, -11947320, -498768, -264360, -559248, 32952432, -2061360, -37128408, -10466400, 18355512

Offset: 1

Author

Jonathan Vos Post, May 24 2006

Keywords

• easy
• sign

Comments

Quadratic analog of A117301 Determinants of 2 X 2 matrices of continuous blocks of 4 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; block 2: 121, 169, 289, 361; and so forth. Through n = 10^6, the number of negative values a(n) in this sequence appears to be consistently larger than the number of positive values.

Examples

			a(1) = -29 =
  | 4   9|
  |25  49|.
		

Crossrefs

Cf. A000040, A001248, A117301.

Programs

Maple

a:= n-> LinearAlgebra[Determinant](Matrix(2, (i,j)-> ithprime(n+2*i-3+j)^2)):
seq(a(n), n=1..32);  # Alois P. Heinz, Jan 25 2021

Mathematica

m = 32; p = Prime[Range[m + 3]]^2; Table[Det @ Partition[p[[n ;; n + 3]], 2], {n, 1, m}] (* Amiram Eldar, Jan 25 2021 *)

PARI

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

Formula

a(n) = prime(n)^2*prime(n+3)^2 - prime(n+1)^2*prime(n+2)^2.