1,1

Semiprime 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 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.

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|.

SemiPrimePi[ n_ ] := Sum[ PrimePi[ n/Prime(AT)i ] - i + 1, {i, PrimePi(AT)Sqrt(AT)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 (rgwv(at)rgwv.com), May 26 2006

Cf. A001358, A067276, A118772, A118779.

Adjacent sequences: A118767 A118768 A118769 this_sequence A118771 A118772 A118773

Sequence in context: A129225 A129226 A003010 this_sequence A112514 A001140 A138488

easy,sign

Jonathan Vos Post (jvospost2(AT)yahoo.com), May 22 2006

More terms from Robert G. Wilson v (rgwv(at)rgwv.com), May 26 2006