A327273 An upper bound sequence for A327272.

1, 5, 105, 425, 144925, 580125, 243697125, 46420625, 253459513125

Offset

0,2

Comments

a(n) can be calculated by a faster algorithm than that for A327272(n). It gives a small (but not necessarily smallest) positive determinant with top row [1,2,2^2,...,2^n] and all entries integers, and rows orthogonal. Note that a(n) = A327272(n) for n=0,1 and 3. See Pinner and Smyth link below for both algorithms, and more details of the sequences.

Links

Table of n, a(n) for n=0..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 0 <= n <= 8

Example

a(2) = 105 since the algorithm for a(n) produces the determinant([[1,2,4],[2,-1,0],[4,8,-5]]) = 105, having top row [1,2,2^2] and all rows orthogonal.

Crossrefs

Sequence in context: A057016 A193340 A083252 * A034225 A273966 A114481

Adjacent sequences: A327270 A327271 A327272 * A327274 A327275 A327276

Keyword

nonn,more

Author

Christopher J. Smyth, Sep 09 2019

Status

approved