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A327269 Smallest modulus of any integer n X n determinant with top row 1,2,...,n and rows nonzero and pairwise orthogonal 3
1, 5, 42, 90, 990, 5733, 6720, 39168 (list; graph; refs; listen; history; text; internal format)



Also a(n) = A327267(p_1...p_n), with p_j = j-th prime, since p_1...p_n is the Heinz code for the multiset {1,2,3,...,n}. For more details see Pinner and Smyth link.


Table of n, a(n) for n=1..8.

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 n <= 8


a(3)=42 since det([1,2,3],[1,-2,1],[4,1,-2]) = 42 and is the smallest positive determinant with top row [1,2,3] and all rows orthogonal.


Subsequence of A327267-- see comments; A327271 is similar, but determinant's top row is n 1's; A327272 is similar, but determinant's top row is 1,2,2^2,...,2^n.

Sequence in context: A216610 A025173 A222474 * A266021 A062021 A241780

Adjacent sequences:  A327266 A327267 A327268 * A327270 A327271 A327272




Christopher J. Smyth, Sep 02 2019



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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)