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A287653
Prime numbers of the form p*q + q*r + r*s with p,q,r,s consecutive primes.
3
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
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
MATHEMATICA
Select[#[[1]]#[[2]]+#[[2]]#[[3]]+#[[3]]#[[4]]&/@Partition[Prime[Range[200]], 4, 1], PrimeQ] (* Harvey P. Dale, Jul 07 2024 *)
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
KEYWORD
nonn
AUTHOR
Zak Seidov, May 29 2017
STATUS
approved