OFFSET
1,1
LINKS
Robert Israel, Table of n, a(n) for n = 1..2000
EXAMPLE
a(1) = 261977 is a term because 261977, 261983 and 262007 are consecutive primes with 261977*261983 + 261977*262007 - 261983*262007 = 68631948349,
261977*261983 - 261977*262007 + 261983*262007 = 68635092433, and
-261977*261983 + 261977*262007 + 261983*262007 = 68647667329 prime.
MAPLE
q:= 2: r:= 3:
R:= NULL: count:= 0:
while count < 40 do
p:= q; q:= r; r:= nextprime(r);
s:= p*(q+r)+q*r;
if isprime(s-2*p*q) and isprime(s-2*p*r) and isprime(s-2*q*r) then R:= R, p; count:= count+1;
fi
od:
R;
MATHEMATICA
f[p_, q_, r_] := PrimeQ[p*q + p*r - q*r] && PrimeQ[p*q - p*r + q*r] && PrimeQ[-p*q + p*r + q*r]; Select[Partition[Prime[Range[10^6]], 3, 1], f @@ # &][[;; , 1]] (* Amiram Eldar, Nov 13 2022 *)
PROG
(Python)
from itertools import islice
from sympy import isprime, nextprime
def agen():
p, q, r = 2, 3, 5
while True:
pq, pr, qr = p*q, p*r, q*r
if all(isprime(t) for t in [pq+pr-qr, pq-pr+qr, -pq+pr+qr]): yield p
p, q, r = q, r, nextprime(r)
print(list(islice(agen(), 15))) # Michael S. Branicky, Nov 13 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Nov 13 2022
STATUS
approved