A351022
Maximal permanent of an n X n symmetric Toeplitz matrix using the first n prime numbers.
Original entry on oeis.org
1, 2, 13, 289, 13814, 1795898, 265709592, 70163924440, 20610999526800, 9097511018219760, 6845834489829830144
Offset: 0
a(3) = 289:
3 5 2
5 3 5
2 5 3
a(4) = 13814:
5 7 3 2
7 5 7 3
3 7 5 7
2 3 7 5
a(5) = 1795898:
5 11 7 3 2
11 5 11 7 3
7 11 5 11 7
3 7 11 5 11
2 3 7 11 5
-
from itertools import permutations
from sympy import Matrix, prime
def A351022(n): return 1 if n == 0 else max(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
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
-
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 *)
-
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
-
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
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.
-
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]]
-
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
-
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
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
-
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]]
-
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
-
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
A351611
Maximal permanent of an n X n symmetric matrix using the integers 1 to n*(n + 1)/2.
Original entry on oeis.org
1, 1, 11, 420, 41451, 7985639, 2779152652
Offset: 0
a(3) = 420:
1 5 6
5 3 4
6 4 2
a(4) = 41451:
1 5 8 10
5 4 9 7
8 9 3 6
10 7 6 2
Showing 1-5 of 5 results.
Comments