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

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A340461 A340462 A340463 * A340465 A340466 A340467

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jan 08 2021

Status

approved