A255871 Numbers prime(n) such that the determinant of the matrix [prime(n), prime(n+1); prime(n+2), prime(n+3)] is positive.

17, 29, 41, 43, 59, 67, 71, 79, 107, 131, 149, 163, 173, 193, 197, 227, 233, 239, 269, 277, 281, 311, 313, 347, 349, 379, 397, 431, 439, 461, 463, 499, 509, 521, 569, 599, 613, 617, 641, 643, 653, 659, 673, 677, 733, 739, 751, 761, 769, 823, 827, 857, 881, 907

Offset

1,1

Comments

Primes prime(n) such that prime(n)*prime(n+3)-prime(n+1)*prime(n+2) is positive.

Links

Table of n, a(n) for n=1..54.

Example

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.

Prog

(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
(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

Crossrefs

Sequence in context: A081985 A087937 A103739 * A196668 A096785 A104228

Adjacent sequences: A255868 A255869 A255870 * A255872 A255873 A255874

Keyword

nonn

Author

Pierandrea Formusa, Mar 08 2015

Status

approved