OFFSET
1,1
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.
FORMULA
a(n) = prime(n)^2*prime(n+3)^2 - prime(n+1)^2*prime(n+2)^2.
EXAMPLE
a(1) = -29 =
| 4 9|
|25 49|.
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 *)
PROG
(PARI) a(n) = prime(n)^2*prime(n+3)^2 - prime(n+1)^2*prime(n+2)^2; \\ Michel Marcus, Jan 25 2021
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Jonathan Vos Post, May 24 2006
STATUS
approved