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Primes p such that the 3 X 3 matrix with components (row by row) prime(k+m), 0 <= m <= 8 has zero determinant, where p = prime(k).
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%I #9 Jan 28 2021 21:41:41

%S 2213,4073,8011,9041,15649,23663,37483,38453,59663,63487,65111,71861,

%T 83557,97157,100279,118801,129527,131707,139291,163601,166597,166799,

%U 180181,180233,195691,203807,209233,217201,227561,238657,289139,309121,327473

%N Primes p such that the 3 X 3 matrix with components (row by row) prime(k+m), 0 <= m <= 8 has zero determinant, where p = prime(k).

%C Primes arising from A117345.

%F a(n) = prime(A117345(n)).

%e The next 8 primes after 2213 are 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, and we have det({{2213, 2221, 2237}, {2239, 2243, 2251}, {2267, 2269, 2273}}) = 0, hence 2213 is a term.

%o (PARI) for(k=1, 35000, M=matrix(3, 3, i, j, prime(k+3*(i-1)+j-1)); if(matdet(M, 1)==0, print1(prime(k), ", ")))

%Y Cf. A117330, A117345, A340923.

%K nonn

%O 1,1

%A _Jianing Song_, Jan 28 2021