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

%I A118781 #11 Nov 29 2015 13:44:29
%S A118781 -196,272,-251,149,-423,909,-408,-452,958,-123,-112,-460,84,-271,-187,
%T A118781 -162,63,7,101,-483,-133,205,-860,-46,339,1178,848,366,1084,719,-384,
%U A118781 334,-2736,-984,-1912,214,34,40,-1735,-60,64,-2263,-3468,5795,69,132,3007,256,2130,3428
%N A118781 Determinants of 3 X 3 matrices of continuous blocks of 9 consecutive semiprimes.
%C A118781 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.
%F A118781 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.
%e A118781 a(1) = -196 because the determinant of the first continuous block of 9 semiprimes is:
%e A118781 | 4. 6. 9.|
%e A118781 |10. 14. 15.|
%e A118781 |21. 22. 25.|.
%e A118781 a(9) = 958 because the determinant of the 9th continuous block of 9 semiprimes is:
%e A118781 |25. 26. 33.|
%e A118781 |34. 35. 38.|
%e A118781 |39. 46. 49.|.
%e A118781 a(50) = 3428 because the determinant of the 50th continuous block of 9 semiprimes is:
%e A118781 |146. 155. 158.|
%e A118781 |159. 161. 166.|
%e A118781 |169. 177. 178.|.
%p A118781 A118781 := proc(n)
%p A118781     local A,i,r,c ;
%p A118781     A := Matrix(3,3) ;
%p A118781     i := n ;
%p A118781     for r from 1 to 3 do
%p A118781     for c from 1 to 3 do
%p A118781         A[r,c] := A001358(i) ;
%p A118781         i := i+1 ;
%p A118781     end do:
%p A118781     end do:
%p A118781     LinearAlgebra[Determinant](A) ;
%p A118781 end proc: # _R. J. Mathar_, May 05 2013
%t A118781 Det/@(Partition[#,3]&/@(Partition[Select[Range[200],PrimeOmega[ #] == 2&],9,1])) (* _Harvey P. Dale_, Nov 29 2015 *)
%Y A118781 Cf. A001358, A067276, A117301, A118713.
%K A118781 easy,sign
%O A118781 1,1
%A A118781 _Jonathan Vos Post_, May 22 2006