A067276
Determinant of n X n matrix containing the first n^2 primes in increasing order.
Original entry on oeis.org
2, -1, -78, 880, -4656, -14304, -423936, 8342720, 711956736, -615707136, 21057138688, -4663930678272, 211912980656128, -9178450735677440, 40005919124799488, 83013253447139328, -8525111273818357760, -800258888289188708352, -15170733077495639179264
Offset: 1
a(3) = -78 because det[[2,7,17],[3,11,19],[5,13,23]] = -78 (= det[[2,3,5],[7,11,13],[17,19,23]], the determinant of the transpose.).
-
[ Determinant( Matrix(n, n, [ NthPrime(k): k in [1..n^2] ]) ): n in [1..19] ]; // Klaus Brockhaus, May 12 2010
-
seq(LinearAlgebra:-Determinant(Matrix(n,n,(i,j) -> ithprime(n*(i-1)+j))),n=1..20); # Robert Israel, Jul 12 2017
-
Table[ Det[ Partition[ Array[Prime, n^2], n]], {n, 19}] (* Robert G. Wilson v, May 26 2006 *)
-
for(n=1,20,k=0; m=matrix(n,n,x,y, prime(k=k+1)); print1(matdet(m), ", ")) /* The matrix initialization command above fills columns first: Variables (such as) x and y take on values 1 through n for rows and columns, respectively, with x changing more rapidly and they must be specified even though the 5th argument is not an explicit function of them here. */
-
from sympy.matrices import Matrix
from sympy import sieve
def a(n):
sieve.extend_to_no(n**2)
return Matrix(n, n, sieve[1:n**2+1]).det()
print([a(n) for n in range(1, 20)]) # Indranil Ghosh, Jul 31 2017
A350858
Minimal permanent of an n X n matrix whose elements are a permutation of the first n^2 prime numbers.
Original entry on oeis.org
1, 2, 29, 3664, 1820642, 2276752048, 5697057180536
Offset: 0
a(2) = 29:
2 3
5 7
a(3) = 3664:
2 3 5
7 13 19
11 17 23
-
from itertools import permutations
from sympy import Matrix
def A350858(n): return 1 if n == 0 else min(Matrix(n,n,p).per() for p in permutations(prime(m) for m in range(1,n**2+1))) # Chai Wah Wu, Jan 21 2022
A350859
Maximal permanent of an n X n matrix whose elements are a permutation of the first n^2 prime numbers.
Original entry on oeis.org
1, 2, 41, 11868, 12124850, 25767879812, 101120963518528
Offset: 0
a(2) = 41:
5 2
3 7
a(3) = 11868:
23 5 3
2 13 19
7 17 11
-
from itertools import permutations
from sympy import Matrix
def A350859(n): return 1 if n == 0 else max(Matrix(n,n,p).per() for p in permutations(prime(m) for m in range(1,n**2+1))) # Chai Wah Wu, Jan 21 2022
A232773
Permanent of the n X n matrix with numbers 1,2,...,n^2 in order across rows.
Original entry on oeis.org
1, 1, 10, 450, 55456, 14480700, 6878394720, 5373548250000, 6427291156586496, 11157501095973529920, 26968983444160450560000, 87808164603589940623344000, 374818412822626584819196231680, 2050842983500342507649178541536000, 14112022767608502582976078751055052800
Offset: 0
-
a:= n-> (-1)^n*add(n^k*Stirling1(n, n-k)*
Stirling1(n+1, k+1)*(n-k)!*k!, k=0..n):
seq(a(n), n=0..20); # Alois P. Heinz, Dec 02 2013
-
Table[(-1)^n * Sum[n^k * StirlingS1[n, n-k] * StirlingS1[n+1, k+1] * (n-k)! * k!,{k,0,n}],{n,0,20}] (* Vaclav Kotesovec after Max Alekseyev, Nov 30 2013 *)
-
a(n) = (-1)^n * sum(k=0,n, n^k * stirling(n,n-k) * stirling(n+1,k+1) * (n-k)! * k! ) /* Max Alekseyev, Nov 30 2013 */
-
from sympy.functions.combinatorial.numbers import stirling, factorial
def A232773(n): return abs(sum(n**k*stirling(n,n-k,kind=1,signed=True)*stirling(n+1,k+1,kind=1,signed=True)*factorial(n-k)*factorial(k) for k in range(n+1))) # Chai Wah Wu, Mar 25 2025
Showing 1-4 of 4 results.
Comments