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A118772
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Determinant of n X n matrix containing the first n^2 3-almost primes in increasing order.
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3
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8, -56, 156, 13328, -920, -83678, 1261988, 54252742, 214409844, -3528354250, 247094703588, -509185323508, 15154985424718, 884710401396570, 49777180907707320, -172913218088289027, 844641410704177098, 3066058962037715903, -33948947842497666568
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 3-almost prime analogue of A067276 Determinant of n X n matrix containing the first n^2 primes in increasing order. The first column contains the first n 3-almost primes in increasing order, the second column contains the next n 3-almost primes in increasing order, etc. Equivalently, first row contains first n 3-almost primes in increasing order, second row contains next n 3-almost primes in increasing order, etc. See also: A118713 a(n) = semiprime circulant.
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EXAMPLE
| a(2) = -56 because of the determinant -56 =
|8, 12|
18, 20|.
a(6) = -83678 because of the determinant -83678 =
| 8, 12, 18, 20, 27, 28|
| 30, 42, 44, 45, 50, 52|
| 63, 66, 68, 70, 75, 76|
| 78, 92, 98, 99, 102, 105|
| 110, 114, 116, 117, 124, 125|
| 130, 138, 147, 148, 153, 154|.
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MATHEMATICA
| ThreeAlmostPrimePi[ n_ ] := Sum[ PrimePi[ n/(Prime(AT)i*Prime(AT)j) ] - j + 1, {i, PrimePi[ n^(1/3) ]}, {j, i, PrimePi(AT)Sqrt[ n/Prime(AT)i ]} ]; ThreeAlmostPrime[ n_ ] := Block[ {e = Floor[ Log[ 2, n ] + 1 ], a, b}, a = 2^e; Do[ b = 2^p; While[ ThreeAlmostPrimePi[ a ] < n, a = a + b ]; a = a - b/2, {p, e, 0, -1} ]; a + b/2 ]; Table[ Det[ Partition[ Array[ ThreeAlmostPrime, n^2 ], n ] ], {n, 19} ] - Robert G. Wilson v (rgwv(at)rgwv.com), May 26 2006
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CROSSREFS
| Cf. A014612, A067276, A118770, A118779.
Sequence in context: A160429 A003722 A044146 * A168013 A003210 A135417
Adjacent sequences: A118769 A118770 A118771 * A118773 A118774 A118775
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KEYWORD
| easy,sign
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), May 22 2006
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(at)rgwv.com), May 26 2006
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