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A067276
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Determinant of n X n matrix containing the first n^2 primes in increasing order.
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10
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2, -1, -78, 880, -4656, -14304, -423936, 8342720, 711956736, -615707136, 21057138688, -4663930678272, 211912980656128, -9178450735677440, 40005919124799488, 83013253447139328, -8525111273818357760, -800258888289188708352, -15170733077495639179264
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The first column contains the first n primes in increasing order, the second column contains the next n primes in increasing order, etc. Equivalently, first row contains first n primes in increasing order, second row contains next n primes in increasing order, etc. Sequences of determinants of matrices specifically containing primes include A024356 (Hankel matrix), A067549 (first n primes on diagonal, other elements 1), A066933 (cyclic permutations of first n primes in each row) and A067551 (first n primes on diagonal, other elements 0).
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EXAMPLE
| a(3) = -78 because det[[2,7,17],[3,11,19],[5,13,23]] = -78 (= det[[2,3,5],[7,11,13],[17,19,23]], the determinant of the transpose.).
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MATHEMATICA
| Table[ Det[ Partition[ Array[Prime, n^2], n]], {n, 19}] (from Robert G. Wilson v (rgwv(at)rgwv.com), May 26 2006)
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PROG
| (PARI) for(n=1, 20, k=0; m=matrix(n, n, x, y, prime(k=k+1)); print(matdet(m))) (The matrix initialization command above fills columns first: Variables (such as) x and y take on values 1 through n for rows and columns, respectively, with x changing more rapidly and they must be specified even though the 5th argument is not an explicit function of them here.).
(MAGMA) [ Determinant( Matrix(n, n, [ NthPrime(k): k in [1..n^2] ]) ): n in [1..19] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 12 2010]
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CROSSREFS
| Cf. A024356, A067549, A066933, A067551.
Cf. A119894, A118770, A118772, A118779.
Sequence in context: A092650 A104024 A096681 * A118580 A118558 A095837
Adjacent sequences: A067273 A067274 A067275 * A067277 A067278 A067279
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KEYWORD
| easy,sign
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Feb 21 2002
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