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A340463
Primes p such that p*q+r*s+t*u is prime, where p,q,r,s,t,u are consecutive primes.
2
3, 17, 41, 47, 67, 107, 193, 197, 199, 211, 229, 239, 313, 331, 367, 461, 467, 503, 523, 571, 919, 929, 991, 1021, 1039, 1093, 1109, 1163, 1193, 1237, 1277, 1327, 1361, 1381, 1621, 1627, 1783, 1901, 2029, 2099, 2143, 2381, 2389, 2423, 2473, 2663, 2677, 2801, 2917, 2939, 2953, 2957, 2963, 3019
OFFSET
1,1
LINKS
EXAMPLE
a(3)=41 is a term because 41*43+47*53+59*61=7853 is prime, where 41,43,47,53,59,61 are consecutive primes.
MAPLE
map(ithprime, select(i -> isprime(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 p <= nn:
if isprime(prod): alst.append(p)
consec6 = consec6[1:] + [nextprime(consec6[-1])]
p, q, r, s, t, u = consec6; prod = p*q+r*s+t*u
return alst
print(aupto(3019)) # Michael S. Branicky, Jan 08 2021
CROSSREFS
Cf. A340464.
Sequence in context: A179783 A196781 A298232 * A107147 A049078 A209544
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jan 08 2021
STATUS
approved