OFFSET
1,1
COMMENTS
Delta = pqr + 2uvw - pu^2 - qv^2 - rw^2.
Using consecutive primes in the general conic section and computing Delta, the value is most often (~98%) > 0.
EXAMPLE
For (p,q,r,u,v,w) = (2,3,5,7,11,13), Delta = 726 > 0. Hence, p=2 (smallest prime) is not in the sequence.
For (p,q,r,u,v,w) = (863,877,881,883,887,907), Delta = -73164 < 0. Hence, p=863 (smallest prime) is a member of the sequence.
MATHEMATICA
Select[Partition[Prime@ Range[3000], 6, 1], Function[{p, q, r, u, v, w}, p q r + 2 u v w - p u^2 - q v^2 - r w^2 < 0] @@ # &][[All, 1]] (* Michael De Vlieger, Sep 30 2019 *)
PROG
(PARI) lista(nn) = {forprime (p=1, nn, q = nextprime(p+1); r = nextprime(q+1); u = nextprime(r+1); v = nextprime(u+1); w = nextprime(v+1); if ((x=p*q*r + 2*u*v*w - p*u^2 - q*v^2 - r*w^2)< 0, print1(p, ", ")); ); } \\ Michel Marcus, Sep 18 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Philip Mizzi, Sep 16 2019
EXTENSIONS
More terms from Michel Marcus, Sep 18 2019
STATUS
approved