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

1,1

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.

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A002808, A117301, A118780.

Sequence in context: A247511 A097824 A133208 * A112124 A268916 A362236

Adjacent sequences: A118874 A118875 A118876 * A118878 A118879 A118880

Keyword

easy,sign

Author

Jonathan Vos Post, May 24 2006

Status

approved