%I #24 Mar 10 2015 09:53:21
%S 17,29,41,43,59,67,71,79,107,131,149,163,173,193,197,227,233,239,269,
%T 277,281,311,313,347,349,379,397,431,439,461,463,499,509,521,569,599,
%U 613,617,641,643,653,659,673,677,733,739,751,761,769,823,827,857,881,907
%N Numbers prime(n) such that the determinant of the matrix [prime(n), prime(n+1); prime(n+2), prime(n+3)] is positive.
%C Primes prime(n) such that prime(n)*prime(n+3)-prime(n+1)*prime(n+2) is positive.
%e 17 belongs to the sequence as 17 is prime, it is the 7th prime, 8th is 19, 9th is 23, 10th is 29, and the matrix [17,19;23,29] has a determinant of 56, which is positive.
%o (Octave) p=primes(1000); for n=1:100 m=[p(n),p(n+1);p(n+2),p(n+3)]; if det(m)>0 disp(p(n)) end end
%o (PARI) lista(nn) = {forprime(p=2, nn, q=nextprime(p+1); r=nextprime(q+1); if (p*nextprime(r+1) - q*r > 0, print1(p, ", ")););} \\ _Michel Marcus_, Mar 09 2015
%K nonn
%O 1,1
%A _Pierandrea Formusa_, Mar 08 2015
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