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A369947 a(n) is the maximal determinant of an n X n Hankel matrix using the first 2*n - 1 prime numbers.

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%I A369947 #17 Feb 12 2024 12:34:33
%S A369947 1,2,11,286,86087,9603283,1764195984
%N A369947 a(n) is the maximal determinant of an n X n Hankel matrix using the first 2*n - 1 prime numbers.
%H A369947 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hankel_matrix">Hankel matrix</a>.
%e A369947 a(2) = 11:
%e A369947   3, 2;
%e A369947   2, 5.
%e A369947 a(3) = 286:
%e A369947    3, 11, 5;
%e A369947   11,  5, 7;
%e A369947    5,  7, 2.
%e A369947 a(4) = 86087:
%e A369947    7,  3, 13, 17;
%e A369947    3, 13, 17,  2;
%e A369947   13, 17,  2, 11;
%e A369947   17,  2, 11,  5.
%t A369947 a[n_] := Max[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]]
%o A369947 (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
%o A369947 (Python)
%o A369947 from itertools import permutations
%o A369947 from sympy import primerange, prime, Matrix
%o A369947 def A369947(n): return max(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
%Y A369947 Cf. A024356, A368352.
%Y A369947 Cf. A369946 (minimal), A350933 (maximal absolute value), A369949, A350940 (maximal permanent).
%K A369947 nonn,hard,more
%O A369947 0,2
%A A369947 _Stefano Spezia_, Feb 06 2024
%E A369947 a(6) from _Michel Marcus_, Feb 08 2024