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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.
3
313, 2137, 7853, 10847, 17911, 43961, 130631, 138239, 145967, 154723, 175463, 192853, 331871, 359377, 436481, 676253, 713807, 824437, 907969, 1037557, 2637959, 2683151, 3050543, 3228437, 3341369, 3676639, 3833723, 4196513, 4412081, 4793713, 4961497, 5614957, 5727791, 5976209, 8122097, 8201213
OFFSET
1,1
LINKS
FORMULA
a(n)=prime(m)*prime(m+1)+prime(m+2)*prime(m+3)+prime(m+4)*prime(m+5) where A340463(n)=prime(m).
EXAMPLE
a(3)=41*43+47*53+59*61=7853, where 41,43,47,53,59,61 are consecutive primes and 7853 is prime.
MAPLE
select(isprime, map(i -> ithprime(i)*ithprime(i+1)+ithprime(i+2)*ithprime(i+3)+ithprime(i+4)*ithprime(i+5), [$1..1000]));
PROG
(Python)
from sympy import nextprime, isprime
def aupto(nn):
alst, consec6 = [], [2, 3, 5, 7, 11, 13]
p, q, r, s, t, u = consec6; prod = p*q+r*s+t*u
while prod <= nn:
if isprime(prod): alst.append(prod)
consec6 = consec6[1:] + [nextprime(consec6[-1])]
p, q, r, s, t, u = consec6; prod = p*q+r*s+t*u
return alst
print(aupto(10**8)) # Michael S. Branicky, Jan 08 2021
CROSSREFS
Cf. A340463.
Sequence in context: A082436 A108845 A348170 * A272442 A200912 A123059
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jan 08 2021
STATUS
approved