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A340464 Primes of the form p*q+r*s+t*u, where p,q,r,s,t,u are consecutive primes.

%I A340464 #15 Jan 10 2021 22:10:30
%S A340464 313,2137,7853,10847,17911,43961,130631,138239,145967,154723,175463,
%T A340464 192853,331871,359377,436481,676253,713807,824437,907969,1037557,
%U A340464 2637959,2683151,3050543,3228437,3341369,3676639,3833723,4196513,4412081,4793713,4961497,5614957,5727791,5976209,8122097,8201213
%N A340464 Primes of the form p*q+r*s+t*u, where p,q,r,s,t,u are consecutive primes.
%H A340464 Robert Israel, <a href="/A340464/b340464.txt">Table of n, a(n) for n = 1..10000</a>
%F A340464 a(n)=prime(m)*prime(m+1)+prime(m+2)*prime(m+3)+prime(m+4)*prime(m+5) where A340463(n)=prime(m).
%e A340464 a(3)=41*43+47*53+59*61=7853, where 41,43,47,53,59,61 are consecutive primes and 7853 is prime.
%p A340464 select(isprime, map(i -> ithprime(i)*ithprime(i+1)+ithprime(i+2)*ithprime(i+3)+ithprime(i+4)*ithprime(i+5), [$1..1000]));
%o A340464 (Python)
%o A340464 from sympy import nextprime, isprime
%o A340464 def aupto(nn):
%o A340464   alst, consec6 = [], [2, 3, 5, 7, 11, 13]
%o A340464   p, q, r, s, t, u = consec6; prod = p*q+r*s+t*u
%o A340464   while prod <= nn:
%o A340464     if isprime(prod): alst.append(prod)
%o A340464     consec6 = consec6[1:] + [nextprime(consec6[-1])]
%o A340464     p, q, r, s, t, u = consec6; prod = p*q+r*s+t*u
%o A340464   return alst
%o A340464 print(aupto(10**8)) # _Michael S. Branicky_, Jan 08 2021
%Y A340464 Cf. A340463.
%K A340464 nonn
%O A340464 1,1
%A A340464 _J. M. Bergot_ and _Robert Israel_, Jan 08 2021