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

Author

Zak Seidov, May 29 2017

Keywords

• nonn

Examples

			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).
		

Links

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

Crossrefs

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

Programs

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

Mathematica

Select[#[[1]]#[[2]]+#[[2]]#[[3]]+#[[3]]#[[4]]&/@Partition[Prime[Range[200]],4,1],PrimeQ] (* Harvey P. Dale, Jul 07 2024 *)

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