A348891
Minimal absolute value of determinant of a nonsingular n X n symmetric Toeplitz matrix using the first n prime numbers.
Original entry on oeis.org
1, 2, 5, 12, 11, 22, 84, 1368, 73, 589, 15057, 2520, 28209
Offset: 0
a(3) = 12:
2 3 5
3 2 3
5 3 2
a(4) = 11:
2 5 3 7
5 2 5 3
3 5 2 5
7 3 5 2
a(5) = 22:
2 3 5 7 11
3 2 3 5 7
5 3 2 3 5
7 5 3 2 3
11 7 5 3 2
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from itertools import permutations
from sympy import Matrix, prime
def A348891(n): return min(d for d in (abs(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))) if d > 0) # Chai Wah Wu, Jan 28 2022
A350955
Minimal determinant of an n X n symmetric Toeplitz matrix using the first n prime numbers.
Original entry on oeis.org
1, 2, -5, -35, -435, -87986, -7186995, -496722800, -68316404507, -9102428703537, -3721326642272925, -488684390484513105, -195315251884652232704
Offset: 0
a(3) = -35:
[3 5 2]
[5 3 5]
[2 5 3]
a(4) = -435:
[5 7 2 3]
[7 5 7 2]
[2 7 5 7]
[3 2 7 5]
a(5) = -87986:
[ 2 3 11 5 7]
[ 3 2 3 11 5]
[11 3 2 3 11]
[ 5 11 3 2 3]
[ 7 5 11 3 2]
-
from itertools import permutations
from sympy import Matrix, prime
def A350955(n): return min(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
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
A350939
Minimal permanent of an n X n Toeplitz matrix using the first 2*n - 1 prime numbers.
Original entry on oeis.org
1, 2, 19, 496, 29609, 3009106, 498206489
Offset: 0
a(2) = 19:
2 3
5 2
a(3) = 496:
2 3 7
5 2 3
11 5 2
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a[n_] := Min[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 (dMichel Marcus, Feb 08 2024
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from itertools import permutations
from sympy import Matrix, prime
def A350939(n): return 1 if n == 0 else min(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
Showing 1-4 of 4 results.
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