|
|
A118875
|
|
Determinant of n-th continuous block of 9 consecutive squares of primes.
|
|
0
|
|
|
-213720, 114432, -548352, 892800, -1774080, -7289856, 10105344, -79557120, -97790976, 171740160, 147556224, 56531520, -380053440, 122206464, -164292480, -958000320, 394761600, 189907200, 1139760000, -3023127360, -1495428480, -4260988800, -14501393280, 7022695680
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
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.
|
|
LINKS
|
|
|
EXAMPLE
|
a(1) = -213720 =
| 4 9 25|
| 49 121 169|
|289 361 529|.
a(2) =
| 9 25 49|
| 121 169 289|
| 361 529 841|.
|
|
MAPLE
|
a:= n-> LinearAlgebra[Determinant](Matrix(3, (i, j)-> ithprime(n+3*i-4+j)^2)):
|
|
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 *)
|
|
PROG
|
(PARI) a(n) = matdet(matrix(3, 3, i, j, prime((n+j-1)+3*(i-1))^2)); \\ Michel Marcus, Jan 25 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,sign
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|