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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.

%I A117345 #13 Jan 25 2021 14:36:27
%S A117345 330,561,1009,1123,1826,2632,3966,4056,6031,6363,6505,7112,8154,9348,
%T A117345 9613,11199,12123,12301,12944,14980,15216,15236,16355,16358,17628,
%U A117345 18287,18737,19378,20228,21113,25155,26733,28203,29007,31620,32181,33245
%N A117345 Indices n such that the 3 X 3 matrix with components (row by row) prime(n+k), 0 <= k <= 8, has zero determinant.
%H A117345 Chai Wah Wu, <a href="/A117345/b117345.txt">Table of n, a(n) for n = 1..10000</a>
%o A117345 (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,",")))}
%o A117345 (Python)
%o A117345 from sympy import nextprime, Matrix
%o A117345 k,A117345_list, plist = 1,[], [2, 3, 5, 7, 11, 13, 17, 19, 23]
%o A117345 while k < 10**7:
%o A117345     if Matrix(plist).reshape(3,3).det() == 0:
%o A117345         A117345_list.append(k)
%o A117345     k,plist = k+1,plist[1:]+[nextprime(plist[-1])] # _Chai Wah Wu_, Jan 25 2021
%K A117345 nonn
%O A117345 1,1
%A A117345 _Cino Hilliard_, Apr 24 2006
%E A117345 Edited by _Klaus Brockhaus_, Apr 28 2006