login
A118877
Determinant of n-th continuous block of 4 consecutive composites.
1
-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
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
KEYWORD
easy,sign
AUTHOR
Jonathan Vos Post, May 24 2006
STATUS
approved