A350933
Maximal determinant of an n X n Toeplitz matrix using the first 2*n - 1 prime numbers.
Original entry on oeis.org
1, 2, 19, 1115, 86087, 9603283, 2307021183, 683793949387
Offset: 0
a(2) = 19:
5 2
3 5
a(3) = 1115:
11 2 5
7 11 2
3 7 11
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a[n_] := Max[Table[Abs[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]] (* Stefano Spezia, Feb 06 2024 *)
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a(n) = my(v=[1..2*n-1], m=-oo, d); forperm(v, p, d = abs(matdet(matrix(n, n, i, j, prime(p[i+j-1])))); if (d>m, m = d)); m; \\ Michel Marcus, Feb 08 2024
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from itertools import permutations
from sympy import Matrix, prime
def A350933(n): return max(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).det() for p in permutations(prime(i) for i in range(1,2*n))) # Chai Wah Wu, Jan 27 2022
A369947
a(n) is the maximal determinant of an n X n Hankel matrix using the first 2*n - 1 prime numbers.
Original entry on oeis.org
1, 2, 11, 286, 86087, 9603283, 1764195984
Offset: 0
a(2) = 11:
3, 2;
2, 5.
a(3) = 286:
3, 11, 5;
11, 5, 7;
5, 7, 2.
a(4) = 86087:
7, 3, 13, 17;
3, 13, 17, 2;
13, 17, 2, 11;
17, 2, 11, 5.
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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]]
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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
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from itertools import permutations
from sympy import primerange, prime, Matrix
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
A369949
a(n) is the number of distinct values of the determinant of an n X n Hankel matrix using the first 2*n - 1 prime numbers.
Original entry on oeis.org
1, 1, 3, 59, 2459, 174063, 19141721
Offset: 0
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a[n_] := CountDistinct[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]]
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a(n) = my(v=[1..2*n-1], list=List()); forperm(v, p, listput(list, matdet(matrix(n, n, i, j, prime(p[i+j-1]))));); #Set(list); \\ Michel Marcus, Feb 08 2024
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from itertools import permutations
from sympy import primerange, prime, Matrix
def A369949(n): return len({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
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