A340464 Primes of the form p*q+r*s+t*u, where p,q,r,s,t,u are consecutive primes.
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
Keywords
Examples
a(3)=41*43+47*53+59*61=7853, where 41,43,47,53,59,61 are consecutive primes and 7853 is prime.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A340463.
Programs
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Maple
select(isprime, map(i -> ithprime(i)*ithprime(i+1)+ithprime(i+2)*ithprime(i+3)+ithprime(i+4)*ithprime(i+5), [$1..1000]));
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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
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).