A351021
Minimal permanent of an n X n symmetric Toeplitz matrix using the first n prime numbers.
Original entry on oeis.org
1, 2, 13, 166, 4009, 169469, 10949857, 1078348288, 138679521597, 24402542896843, 5348124003487173
Offset: 0
a(3) = 166:
3 2 5
2 3 2
5 2 3
a(4) = 4009:
3 2 5 7
2 3 2 5
5 2 3 2
7 5 2 3
a(5) = 169469:
5 2 3 7 11
2 5 2 3 7
3 2 5 2 3
7 3 2 5 2
11 7 3 2 5
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from itertools import permutations
from sympy import Matrix, prime
def A351021(n): return 1 if n == 0 else min(Matrix([p[i:0:-1]+p[0:n-i] for i in range(n)]).per() for p in permutations(prime(i) for i in range(1,n+1))) # Chai Wah Wu, Jan 31 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
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
A369952
a(n) is the number of distinct values of the permanent of an n X n Hankel matrix using the first 2*n - 1 prime numbers.
Original entry on oeis.org
1, 1, 2, 59, 2493, 180932, 19939272
Offset: 0
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a[n_] := CountDistinct[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]]
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a(n) = my(v=[1..2*n-1], list=List()); forperm(v, p, listput(list, matpermanent(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 A369952(n): return len({Matrix([p[i:i+n] for i in range(n)]).per() for p in permutations(primerange(prime((n<<1)-1)+1))}) if n else 1 # Chai Wah Wu, Feb 12 2024
A351610
Minimal permanent of an n X n symmetric matrix using the integers 1 to n*(n + 1)/2.
Original entry on oeis.org
1, 1, 7, 163, 9850, 1243806, 284995981
Offset: 0
a(3) = 163:
1 2 3
2 5 4
3 4 6
a(4) = 9850:
1 2 3 4
2 8 5 6
3 5 9 7
4 6 7 10
Showing 1-5 of 5 results.
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