A350956
Maximal determinant of an n X n symmetric Toeplitz matrix using the first n prime numbers.
Original entry on oeis.org
1, 2, 5, 64, 1107, 160160, 5713367, 889747443, 62837596341, 11671262491586, 3090090680653053, 635672008069583520, 278356729040728193703
Offset: 0
a(3) = 64:
[5 2 3]
[2 5 2]
[3 2 5]
a(4) = 1107:
[3 2 7 5]
[2 3 2 7]
[7 2 3 2]
[5 7 2 3]
a(5) = 160160:
[ 5 11 2 3 7]
[11 5 11 2 3]
[ 2 11 5 11 2]
[ 3 2 11 5 11]
[ 7 3 2 11 5]
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from itertools import permutations
from sympy import Matrix, prime
def A350956(n): return max(Matrix([p[i:0:-1]+p[0:n-i] for i in range(n)]).det() for p in permutations(prime(i) for i in range(1,n+1))) # Chai Wah Wu, Jan 27 2022
A350940
Maximal permanent of an n X n Toeplitz matrix using the first 2*n - 1 prime numbers.
Original entry on oeis.org
1, 2, 31, 2364, 346018, 82285908, 39135296624
Offset: 0
a(2) = 31:
5 2
3 5
a(3) = 2364:
11 5 3
7 11 5
2 7 11
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a[n_] := Max[Table[Permanent[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 = matpermanent(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 A350940(n): return 1 if n == 0 else max(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).per() for p in permutations(prime(i) for i in range(1,2*n))) # Chai Wah Wu, Jan 27 2022
A350932
Minimal determinant of an n X n Toeplitz matrix using the first 2*n - 1 prime numbers, with a(0) = 1.
Original entry on oeis.org
1, 2, -11, -286, -57935, -5696488, -1764195984, -521528189252
Offset: 0
a(2) = -11:
2 3
5 2
a(3) = -286:
5 7 2
11 5 7
3 11 5
-
f:= proc(n) local i;
min(map(t -> LinearAlgebra:-Determinant(LinearAlgebra:-ToeplitzMatrix(t)), combinat:-permute([seq(ithprime(i),i=1..2*n-1)]))) end proc:
f(0):= 1:
map(f, [$0..5]); # Robert Israel, Apr 01 2024
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from itertools import permutations
from sympy import Matrix, prime
def A350932(n): return min(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
A351609
Maximal absolute value of the determinant of an n X n symmetric matrix using the integers 1 to n*(n + 1)/2.
Original entry on oeis.org
1, 1, 7, 152, 7113, 745285, 94974369
Offset: 0
a(3) = 152:
2 4 6
4 5 1
6 1 3
a(4) = 7113:
2 6 8 9
6 5 10 1
8 10 3 4
9 1 4 7
A369946
a(n) is the minimal determinant of an n X n Hankel matrix using the first 2*n - 1 prime numbers.
Original entry on oeis.org
1, 2, -19, -1115, -57935, -5696488, -2307021183
Offset: 0
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.
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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]]
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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 (dMichel Marcus, Feb 08 2024
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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
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
-
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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