%I #15 May 11 2021 09:02:32
%S 6,7,9,10,12,13,15,19,21,31,33,34,43,46,51,55,56,58,63,66,68,76,86,90,
%T 121,123,136,161,162,169,174,181,182,211,218,230,238,248,253,255,262,
%U 264,287,291,294,300,305,312
%N Indices k such that scalar product (p,q,r).(s,t,u) = p*s+q*t+r*u is prime, where (p,q,r,s,t,u) are 6 consecutive primes starting with p=prime(k).
%C Corresponding resulting primes: 1381,1933,3373,4261,6449,7577,10607,17683,22543,57859,..,
%e k=6 is a term because (13,17,19)*(23,29,31) = 13*23+17*29+19*31 = 1381 is prime.
%t Select[Range[1000],PrimeQ[{Prime[#],Prime[#+1],Prime[#+2]}.{Prime[#+3],Prime[#+4],Prime[#+5]}]&]
%o (PARI) list(lim)=my(v=List(),p=2,q=3,r=5,s=7,t=11,n); forprime(u=13,, if(n++>lim, break); if(isprime(p*s+q*t+r*u), listput(v,n)); p=q; q=r; r=s; s=t; t=u); Vec(v) \\ _Charles R Greathouse IV_, Mar 20 2017
%o (Python)
%o from sympy import prime, isprime
%o print([n for n in range(1, 501) if isprime(prime(n)*prime(n+3) + prime(n+1)*prime(n+4) + prime(n+2)*prime(n+5))]) # _Indranil Ghosh_, Mar 20 2017
%K nonn
%O 1,1
%A _Zak Seidov_, Mar 20 2017
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