A284094 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).

6, 7, 9, 10, 12, 13, 15, 19, 21, 31, 33, 34, 43, 46, 51, 55, 56, 58, 63, 66, 68, 76, 86, 90, 121, 123, 136, 161, 162, 169, 174, 181, 182, 211, 218, 230, 238, 248, 253, 255, 262, 264, 287, 291, 294, 300, 305, 312

Offset

1,1

Comments

Corresponding resulting primes: 1381,1933,3373,4261,6449,7577,10607,17683,22543,57859,..,

Links

Table of n, a(n) for n=1..48.

Example

k=6 is a term because (13,17,19)*(23,29,31) = 13*23+17*29+19*31 = 1381 is prime.

Mathematica

Select[Range[1000], PrimeQ[{Prime[#], Prime[#+1], Prime[#+2]}.{Prime[#+3], Prime[#+4], Prime[#+5]}]&]

Prog

(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
(Python)
from sympy import prime, isprime
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

Crossrefs

Sequence in context: A348465 A102740 A248178 * A120183 A032710 A188055

Adjacent sequences: A284091 A284092 A284093 * A284095 A284096 A284097

Keyword

nonn

Author

Zak Seidov, Mar 20 2017

Status

approved