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Search: id:A118780
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| A118780 |
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Semiprime(n)*semiprime(n+3) - semiprime(n+1)*semiprime(n+2), where semiprime(n) is the nth semiprime. |
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+0
3
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| -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; listen)
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OFFSET
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1,1
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COMMENT
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Semiprime analogue 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 (mathar(AT)strw.leidenuniv.nl), Nov 27 2007
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FORMULA
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a(n) = A001358(n)*A001358(n+3) - A001358(n+1)*A001358(n+2).
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EXAMPLE
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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.|.
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MAPLE
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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 (mathar(AT)strw.leidenuniv.nl), Nov 27 2007
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CROSSREFS
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Cf. A001358, A067276, A117301, A118713.
Sequence in context: A084676 A068609 A166208 this_sequence A051655 A048932 A033334
Adjacent sequences: A118777 A118778 A118779 this_sequence A118781 A118782 A118783
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KEYWORD
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easy,sign
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), May 22 2006
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EXTENSIONS
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Better definition from Jens Kruse Andersen (jens.k.a(AT)get2net.dk), May 03 2008
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