A118781 Determinants of 3 X 3 matrices of continuous blocks of 9 consecutive semiprimes.

-196, 272, -251, 149, -423, 909, -408, -452, 958, -123, -112, -460, 84, -271, -187, -162, 63, 7, 101, -483, -133, 205, -860, -46, 339, 1178, 848, 366, 1084, 719, -384, 334, -2736, -984, -1912, 214, 34, 40, -1735, -60, 64, -2263, -3468, 5795, 69, 132, 3007, 256, 2130, 3428

Offset: 1

Author

Jonathan Vos Post, May 22 2006

Keywords

• easy
• sign

Comments

Semiprime analog of A117330 Determinants of 3 X 3 matrices of continuous blocks of 9 consecutive primes. The terminology "continuous" is used to distinguish from "discrete" which would be (in this 3 X 3 semiprime case) block 1: 4, 6, 9, 10, 14, 15, 21, 22, 25; block 2: 26, 33, 34, 35, 38, 39, 46, 49, 51; and so forth.

Examples

			a(1) = -196 because the determinant of the first continuous block of 9 semiprimes is:
| 4. 6. 9.|
|10. 14. 15.|
|21. 22. 25.|.
a(9) = 958 because the determinant of the 9th continuous block of 9 semiprimes is:
|25. 26. 33.|
|34. 35. 38.|
|39. 46. 49.|.
a(50) = 3428 because the determinant of the 50th continuous block of 9 semiprimes is:
|146. 155. 158.|
|159. 161. 166.|
|169. 177. 178.|.
		

Crossrefs

Cf. A001358, A067276, A117301, A118713.

Programs

Maple

A118781 := proc(n)
    local A,i,r,c ;
    A := Matrix(3,3) ;
    i := n ;
    for r from 1 to 3 do
    for c from 1 to 3 do
        A[r,c] := A001358(i) ;
        i := i+1 ;
    end do:
    end do:
    LinearAlgebra[Determinant](A) ;
end proc: # R. J. Mathar, May 05 2013

Mathematica

Det/@(Partition[#,3]&/@(Partition[Select[Range[200],PrimeOmega[ #] == 2&],9,1])) (* Harvey P. Dale, Nov 29 2015 *)

Formula

a(n) = s(n)*s(n+4)*s(n+8) - s(n)*s(n+5)*s(n+7) - s(n+1)*s(n+3)*s(n+8) + s(n+1)*s(n+5)*s(n+6) + s(n+2)*s(n+3)*s(n+7) - s(n+2)*s(n+4)*s(n+6) where s(n) = A001358(n) is the n-th semiprime.