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A117345
Indices n such that the 3 X 3 matrix with components (row by row) prime(n+k), 0 <= k <= 8, has zero determinant.
5
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
1,1
PROG
(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
CROSSREFS
Sequence in context: A174848 A300009 A244264 * A237189 A064262 A126997
KEYWORD
nonn
AUTHOR
Cino Hilliard, Apr 24 2006
EXTENSIONS
Edited by Klaus Brockhaus, Apr 28 2006
STATUS
approved