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A369946
a(n) is the minimal determinant of an n X n Hankel matrix using the first 2*n - 1 prime numbers.
4
1, 2, -19, -1115, -57935, -5696488, -2307021183
OFFSET
0,2
EXAMPLE
a(2) = -19:
2, 5;
5, 3.
a(3) = -1115:
3, 7, 11;
7, 11, 2;
11, 2, 5.
a(4) = -57935:
7, 5, 17, 2;
5, 17, 2, 3;
17, 2, 3, 11;
2, 3, 11, 13.
MATHEMATICA
a[n_] := Min[Table[Det[HankelMatrix[Join[Drop[per = Part[Permutations[Prime[Range[2 n - 1]]], i], n], {Part[per, n]}], Join[{Part[per, n]}, Drop[per, - n]]]], {i, (2 n - 1) !}]]; Join[{1}, Array[a, 5]]
PROG
(PARI) a(n) = my(v=[1..2*n-1], m=+oo, d); forperm(v, p, d = matdet(matrix(n, n, i, j, prime(p[i+j-1]))); if (d<m, m = d)); m; \\ Michel Marcus, Feb 08 2024
(Python)
from itertools import permutations
from sympy import primerange, prime, Matrix
def A369946(n): return min(Matrix([p[i:i+n] for i in range(n)]).det() for p in permutations(primerange(prime((n<<1)-1)+1))) if n else 1 # Chai Wah Wu, Feb 12 2024
CROSSREFS
Cf. A369947 (maximal), A350933 (maximal absolute value), A369949, A350939 (minimal permanent).
Sequence in context: A012956 A012976 A013107 * A350933 A172028 A365050
KEYWORD
sign,hard,more
AUTHOR
Stefano Spezia, Feb 06 2024
EXTENSIONS
a(6) from Michel Marcus, Feb 08 2024
STATUS
approved