A367077 Determinant of the n X n matrix whose terms are the n^2 values of isprime(x) from 1 to n^2.
0, -1, -1, 0, 1, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, -15, 0, 0, 0, 0, 0, 400, 0, -196, 0, 0, 0, 0, 0, 4224, 0, 0, 0, -44304, 0, -537138, 0, 0, 0, -4152330, 0, 0, 0, 0, 0, -59171526, 0, 0, 0, 0, 0, -1681340912, 0, 330218571840, 0, 0, 0, 0, 0, -349982854480, 0, 0, 0
Offset: 1
Keywords
Examples
For n=4, we consider the first n^2=16 terms of the characteristic function of primes (A010051): (0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0). These terms form a matrix by arranging them in 4 consecutive subsequences of 4 terms each: 0, 1, 1, 0; 1, 0, 1, 0; 0, 0, 1, 0; 1, 0, 0, 0; and the determinant of this matrix is zero, so a(4)=0.
Programs
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Mathematica
mat[n_,i_,j_]:=Boole[PrimeQ[(i-1)*n+j]]; a[n_]:=Det@Table[mat[n,i,j],{i,1,n},{j,1,n}]; Table[a[n],{n,1,70}] -
PARI
a(n) = matdet(matrix(n, n, i, j, isprime((i-1)*n+j))); \\ Michel Marcus, Nov 07 2023
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Python
from sympy import Matrix, isprime def A367077(n): return Matrix(n,n,[int(isprime(i)) for i in range(1,n**2+1)]).det() # Chai Wah Wu, Nov 16 2023
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