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A118770
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Determinant of n X n matrix containing the first n^2 semiprimes in increasing order.
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5
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4, -14, -196, 480, 696, -57901, -525364, -409579, 18528507, -237549252, -2119519900, 6713972874, 18262155072, -19072020914992, 162234208372185, 1471912942112734, 6828673030820538, -35126752028893500, 729026655790306778, -15365360727898374618
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OFFSET
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1,1
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COMMENTS
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Semiprime analog of A067276 Determinant of n X n matrix containing the first n^2 primes in increasing order. The first column contains the first n semiprimes in increasing order, the second column contains the next n semiprimes in increasing order, etc. Equivalently, first row contains first n semiprimes in increasing order, second row contains next n semiprimes in increasing order, etc. See also: A118713 a(n) = determinant of n X n circulant matrix whose first row is A001358(1), A001358(2), ..., A001358(n) where A001358(n) = n-th semiprime.
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LINKS
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EXAMPLE
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a(2) = -14 because of the determinant -14 =
|4,6 |
|9,10|.
a(6) = -57901 = the determinant
|4, 6, 9, 10, 14, 15,|
|21, 22, 25, 26, 33, 34,|
|35, 38, 39, 46, 49, 51,|
|55, 57, 58, 62, 65, 69,|
|74, 77, 82, 85, 86, 87,|
|91, 93, 94, 95, 106, 111|.
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MATHEMATICA
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SemiPrimePi[ n_ ] := Sum[ PrimePi[ n/Prime @ i ] - i + 1, {i, PrimePi @ Sqrt @ n} ]; SemiPrime[ n_ ] := Block[ {e = Floor[ Log[ 2, n ] + 1 ], a, b}, a = 2^e; Do[ b = 2^p; While[ SemiPrimePi[ a ] < n, a = a + b ]; a = a - b/2, {p, e, 0, -1} ]; a + b/2 ]; Table[ Det[ Partition[ Array[ SemiPrime, n^2 ], n ] ], {n, 20} ] (* Robert G. Wilson v, May 26 2006 *)
Module[{nn=5000, spr}, spr=Select[Range[nn], PrimeOmega[#]==2&]; Table[Det[ Partition[ Take[spr, n^2], n]], {n, Sqrt[Length[spr]]}]] (* Harvey P. Dale, Nov 21 2018 *)
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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