A118875 - OEIS

%I #17 Jan 25 2021 08:59:50

%S -213720,114432,-548352,892800,-1774080,-7289856,10105344,-79557120,

%T -97790976,171740160,147556224,56531520,-380053440,122206464,

%U -164292480,-958000320,394761600,189907200,1139760000,-3023127360,-1495428480,-4260988800,-14501393280,7022695680

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

%C 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.

%e a(1) = -213720 =

%e   |  4    9   25|

%e   | 49  121  169|

%e   |289  361  529|.

%e a(2) =

%e   |   9  25  49|

%e   | 121 169 289|

%e   | 361 529 841|.

%p a:= n-> LinearAlgebra[Determinant](Matrix(3, (i,j)-> ithprime(n+3*i-4+j)^2)):

%p seq(a(n), n=1..25);  # _Alois P. Heinz_, Jan 25 2021

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

%o (PARI) a(n) = matdet(matrix(3, 3, i, j, prime((n+j-1)+3*(i-1))^2)); \\ _Michel Marcus_, Jan 25 2021

%Y Cf. A000040, A001248, A117301, A117330.

%K easy,sign

%O 1,1

%A _Jonathan Vos Post_, May 24 2006

%E Wrong Formula and data corrected by _Michel Marcus_, Jan 25 2021