A118877 - OEIS

%I #13 Aug 03 2020 19:49:17

%S -12,-12,6,6,-18,-18,12,12,-24,-24,18,-3,-28,-2,-2,24,24,-36,-36,-2,

%T -2,32,-3,-42,36,36,-48,-48,42,-3,-52,-2,-2,48,-3,-58,-2,-2,54,54,-66,

%U -66,-2,-2,62,-3,-72,66,66,-78,-78,-2,-2,74,-3,-84,78,-3,-88,-2,-2

%N Determinant of n-th continuous block of 4 consecutive composites.

%C Composites analog of A117301 Determinants of 2 X 2 matrices of continuous blocks of 4 consecutive primes. See also: A118780 Determinants of 2 X 2 matrices of continuous blocks of 4 consecutive semiprimes. The terminology "continuous" is used to distinguish from "discrete" which would be (in this composites case) block 1: 4, 6, 8, 9; block 2: 10, 12, 14, 15 and so forth. It is not until a(12) that we break the pattern of a(2n)=a(2n-1); there seem to be strangely many such pairs of two identical values. a(12) is also the first odd value in the sequence and the first prime.

%H Harvey P. Dale, <a href="/A118877/b118877.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A002808(n)*A002808(n+3) - A002808(n+1)*A002808(n+2).

%e a(1) = -12 =

%e |4 6|

%e |8 9|.

%t Module[{nn=100,cmps},cmps=Select[Range[nn],CompositeQ];Det[ ArrayReshape[ #,{2,2}]]&/@Table[Take[cmps,{n,n+3}],{n,Length[cmps]-3}]] (* _Harvey P. Dale_, Aug 03 2020 *)

%Y Cf. A002808, A117301, A118780.

%K easy,sign

%O 1,1

%A _Jonathan Vos Post_, May 24 2006