A024356
Determinant of Hankel matrix of the first 2n-1 prime numbers.
Original entry on oeis.org
1, 2, 1, -2, 0, 288, -1728, -26240, 222272, 1636864, -8434688, -61820416, 238704640, 544024576, 3294658560, -71814283264, 359994671104, 17294535000064, 302441193013248, -2311203985948672, -11313883306262528, -31078379553816576, 26574426771056230400
Offset: 0
a(2) = 1 because det[[2,3],[3,5]] = 1.
From _Klaus Brockhaus_, May 12 2010: (Start)
a(5) = determinant(M) = 288 where M is the matrix
[ 2 3 5 7 11]
[ 3 5 7 11 13]
[ 5 7 11 13 17]
[ 7 11 13 17 19]
[11 13 17 19 23] . (End)
-
Hankel_prime:=function(n); M:=ScalarMatrix(n, 0); for j in [1..n] do for k in [1..n] do M[j, k]:=NthPrime(j+k-1); end for; end for; return M; end function; [ Determinant(Hankel_prime(n)): n in [0..22] ];
[1] cat [ Determinant( SymmetricMatrix( &cat[ [ NthPrime(j+k-1): k in [1..j] ]: j in [1..n] ] ) ): n in [1..22] ]; // Klaus Brockhaus, May 12 2010
-
a[n_]:=Det[Table[Prime[i+j-1],{i,n},{j,n}]]; Join[{1},Array[a, 20]] (* Stefano Spezia, Feb 03 2024 *)
-
for (i=0,20,print1(","matdet(matrix(i,i,X,Y,prime(X+Y-1))))) \\ Jon Perry, Mar 22 2004
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
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
-
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 *)
-
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
-
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
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
Showing 1-4 of 4 results.
Comments