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A118780 Semiprime(n)*semiprime(n+3) - semiprime(n+1)*semiprime(n+2), where semiprime(n) is the n-th semiprime. 3
-14, -6, -5, 0, -7, -87, -4, 76, -8, -212, 64, -4, 128, 68, -265, 31, -12, -177, 104, 109, -28, 103, -101, -40, -24, -348, -176, 253, 81, -285, -97, 928, 364, -841, -257, -361, -127, -3, -125, 603, 359, -675, 367, -8, -860, 139, -3, 995, 280, -1276, -167, 629, 145, 443, -365, -579, 171, -569 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Semiprime analog of A117301.

By construction, every entry is also the difference between two 4-almost primes: a(1) = A014613(4)-A014613(5); a(2) = A014613(9)-A014613(11); a(3) = A014613(16)-A014613(18); a(4) = A014613(27)-A014613(27); etc. - R. J. Mathar, Nov 27 2007

LINKS

Table of n, a(n) for n=1..58.

FORMULA

a(n) = A001358(n)*A001358(n+3) - A001358(n+1)*A001358(n+2).

EXAMPLE

a(1) = -14 because the determinant of the first block of 4 consecutive semiprimes is:

|4. 6.|

|9. 10|.

a(4) = 0 because the determinant of the 4th block of 4 semiprimes is the first of a presumably infinite number of singular matrices:

|10. 14.|

|15. 21.|.

a(8) = 76, the first positive value in the sequence:

|22. 25.|

|26. 33.|.

MAPLE

A001358 := proc(n) option remember ; local a; if n = 1 then 4 ; else for a from A001358(n-1)+1 do if numtheory[bigomega](a)= 2 then RETURN(a) ; fi ; od: fi ; end: A118780 := proc(n) A001358(n)*A001358(n+3)-A001358(n+1)*A001358(n+2) ; end: seq(A118780(n), n=1..58) ; # R. J. Mathar, Nov 27 2007

CROSSREFS

Cf. A001358, A067276, A117301, A118713.

Sequence in context: A166208 A239863 A294899 * A220672 A051655 A048932

Adjacent sequences:  A118777 A118778 A118779 * A118781 A118782 A118783

KEYWORD

easy,sign

AUTHOR

Jonathan Vos Post, May 22 2006

EXTENSIONS

Better definition from Jens Kruse Andersen, May 03 2008

STATUS

approved

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Last modified October 15 07:46 EDT 2019. Contains 328026 sequences. (Running on oeis4.)