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 A327272 Smallest modulus of any (n+1) X (n+1) integer determinant whose top row is 1,2,2^2,...,2^n and whose rows are pairwise orthogonal. 4
 1, 5, 42, 425, 17050, 54600, 11468100 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS An algorithm for generating a(n) is given in the Pinner and Smyth link, where more details about a(n) can be found. Also, see file link below for {(n,a(n),matrix(n)),0 <= n <= 6}, where matrix(n) has minimal modulus determinant equal to a(n) among (n+1) X (n+1) matrices with top row 1,2,2^2,...,2^n and all rows orthogonal. LINKS Chris Pinner and Chris Smyth, Lattices of minimal index in Z^n having an orthogonal basis containing a given basis vector Christopher J. Smyth, List of n, a(n) and associated matrix for 0 <= n <= 6 FORMULA a(n) = A327267(Product_{k=0..n} prime(2^k)) = A327267(A325782(n+1)). EXAMPLE a(2) =42 since det([[1,2,4],[2,-3,1],[2,1,-1]]) = 42 and is the smallest positive determinant with top row [1,2,2^2] and all entries integers, and rows orthogonal. CROSSREFS Subsequence of A327267-- see comments; A327269 is similar, but determinant's top row is 1,2,...,n; A327271 is similar, but determinant's top row consists of n 1's. Sequence in context: A126765 A228793 A330628 * A024492 A217805 A217808 Adjacent sequences:  A327269 A327270 A327271 * A327273 A327274 A327275 KEYWORD nonn,more AUTHOR Christopher J. Smyth, Sep 09 2019 STATUS approved

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Last modified February 26 01:28 EST 2020. Contains 332270 sequences. (Running on oeis4.)