A358382 First of three consecutive primes p,q,r such that r*(p+q) + p*q and r*(p+q) - p*q are prime.

2, 3, 5, 7, 29, 43, 277, 283, 773, 967, 2801, 3391, 3701, 5189, 5233, 5531, 5591, 6869, 6949, 7043, 7753, 9419, 9787, 10091, 10957, 11173, 11551, 13577, 13729, 13781, 15319, 15383, 17489, 17509, 18583, 19141, 22091, 23029, 23669, 25523, 25601, 25693, 26249, 27077, 31151, 31469, 31891, 32257

Offset

1,1

Links

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

Example

a(4) = 7 is a term because 7, 11, 13 are consecutive primes with 13*(7+11) + 7*11 = 311 and 13*(7+11) - 7*11 = 157 are prime.

Maple

q:= 2: r:= 3: count:= 0: R:= NULL:
while count < 100 do
  p:= q; q:= r; r:= nextprime(r);
  if isprime(r*(p+q)+p*q) and isprime(r*(p+q)-p*q) then
     R:= R, p; count:= count+1
  fi
od:
R;

Mathematica

Select[Partition[Prime[Range[3500]], 3, 1], PrimeQ[(s = #[[3]]*(#[[1]] + #[[2]])) + (t = #[[1]]*#[[2]])] && PrimeQ[s - t] &][[;; , 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:
        rpq, pq = r*(p+q), p*q
        if all(isprime(t) for t in [rpq+pq, rpq-pq]): yield p
        p, q, r = q, r, nextprime(r)
print(list(islice(agen(), 48))) # Michael S. Branicky, Nov 20 2022

Crossrefs

Sequence in context: A019372 A117299 A091924 * A069108 A156604 A046864

Adjacent sequences: A358379 A358380 A358381 * A358383 A358384 A358385

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Nov 12 2022

Status

approved