A118877 Determinant of n-th continuous block of 4 consecutive composites.

-12, -12, 6, 6, -18, -18, 12, 12, -24, -24, 18, -3, -28, -2, -2, 24, 24, -36, -36, -2, -2, 32, -3, -42, 36, 36, -48, -48, 42, -3, -52, -2, -2, 48, -3, -58, -2, -2, 54, 54, -66, -66, -2, -2, 62, -3, -72, 66, 66, -78, -78, -2, -2, 74, -3, -84, 78, -3, -88, -2, -2

Offset: 1

Author

Jonathan Vos Post, May 24 2006

Keywords

• easy
• sign

Comments

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.

Examples

			a(1) = -12 =
|4 6|
|8 9|.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002808, A117301, A118780.

Programs

Mathematica

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 *)

Formula

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