A117345 Indices n such that the 3 X 3 matrix with components (row by row) prime(n+k), 0 <= k <= 8, has zero determinant.

330, 561, 1009, 1123, 1826, 2632, 3966, 4056, 6031, 6363, 6505, 7112, 8154, 9348, 9613, 11199, 12123, 12301, 12944, 14980, 15216, 15236, 16355, 16358, 17628, 18287, 18737, 19378, 20228, 21113, 25155, 26733, 28203, 29007, 31620, 32181, 33245

Offset: 1

Author

Cino Hilliard, Apr 24 2006

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Programs

PARI

{m=35000;for(n=1,m,M=matrix(3,3,i,j,prime(n+3*(i-1)+j-1));if(matdet(M,1)==0,print1(n,",")))}

Python

from sympy import nextprime, Matrix
k,A117345_list, plist = 1,[], [2, 3, 5, 7, 11, 13, 17, 19, 23]
while k < 10**7:
    if Matrix(plist).reshape(3,3).det() == 0:
        A117345_list.append(k)
    k,plist = k+1,plist[1:]+[nextprime(plist[-1])] # Chai Wah Wu, Jan 25 2021

Extensions

Edited by Klaus Brockhaus, Apr 28 2006