A287653 Prime numbers of the form p*q + q*r + r*s with p,q,r,s consecutive primes.

127, 1427, 2003, 2713, 7639, 76519, 81703, 139663, 166643, 173777, 349589, 371027, 653357, 696083, 752033, 793699, 883549, 938617, 974713, 1150733, 1176983, 1207223, 1310779, 1675577, 1702577, 1880363, 2715169

Offset

1,1

Links

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

Example

a(1) = 127 = 3*5 + 5*7 + 7*11 =
A000040(2)*A000040(3) + A000040(3)*A000040(4) + A000040(4)*A000040(5) =
A006094(2) + A006094(3) + A006094(4).

Maple

N:= 100: # to get a(1) - a(N)
p:= 2: q:= 3: r:= 5: s:= 7:
count:= 0:
while count < N do
  p:= q; q:= r; r:= s; s:= nextprime(s);
  n:= p*q+q*r+r*s;
  if isprime(n) then count:= count+1; A[count]:= n fi
od:
seq(A[i], i=1..N); # Robert Israel, May 29 2017

Prog

(PARI) {p=2; q=3; r=5; s=7; for(k=1, 1000, if(isprime(a=p*q+q*r+r*s),
print1(a", ")); p=q; q=r; r=s; s=nextprime(1+s))}
(Python)
from sympy import nextprime, isprime
A287653_list, pq, qr, rs, s = [], 6, 15, 35, 7
while s <= 10**6:
    n = pq+qr+rs
    if isprime(n):
        A287653_list.append(n)
    t = nextprime(s)
    pq, qr, rs, s = qr, rs, s*t, t # Chai Wah Wu, May 29 2017

Crossrefs

Cf. A000040 (prime numbers), A006094 (products of 2 successive primes).

Sequence in context: A299718 A300339 A189026 * A371337 A258012 A258002

Adjacent sequences: A287650 A287651 A287652 * A287654 A287655 A287656

Keyword

nonn

Author

Zak Seidov, May 29 2017

Status

approved