This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A374242 #13 Oct 10 2024 07:24:49
%S A374242 1,1,3,9,3,1,5,9,1,1,1,1
%N A374242 a(n) is the minimal absolute value of the determinant of a nonsingular n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
%C A374242 The offset is 3 because for n = 2 the unique symmetric Toeplitz matrix having 1 on the main diagonal and 1 off-diagonal is singular.
%C A374242 Conjecture: all the terms are odd.
%H A374242 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A374239%2B40%2B41%2B42.py">Python program</a>.
%H A374242 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.
%e A374242 a(5) = 3:
%e A374242 [1, 1, 2, 3, 4]
%e A374242 [1, 1, 1, 2, 3]
%e A374242 [2, 1, 1, 1, 2]
%e A374242 [3, 2, 1, 1, 1]
%e A374242 [4, 3, 2, 1, 1]
%t A374242 a[n_]:=Min[Select[Table[Abs[Det[ToeplitzMatrix[Join[{1}, Part[Permutations[Range[n - 1]], i]]]]], {i, (n-1)!}],Positive]]; Array[a, 8, 3]
%Y A374242 Cf. A356865, A374139.
%Y A374242 Cf. A374239 (minimal), A374240 (maximal), A374241 (maximal absolute value).
%K A374242 nonn,hard,more
%O A374242 3,3
%A A374242 _Stefano Spezia_, Jul 01 2024
%E A374242 a(11)-a(14) from _Lucas A. Brown_, Oct 10 2024