A338567 Primes p such that (q*r) mod p is prime, where q and r are the next primes after p.

3, 5, 7, 13, 19, 23, 31, 89, 199

Offset

1,1

Comments

a(10) > 2*10^10 if it exists. - Michael S. Branicky, Mar 05 2021

Links

Table of n, a(n) for n=1..9.

Example

a(4)=13 is in the sequence because it is prime, the next two primes are 17 and 19, and (17*19) mod 13 = 11, which is prime.

Maple

R:= NULL: q:= 2: r:= 3:
count:= 0:
for i from 1 to 10000 do
  p:= q; q:= r; r:= nextprime(r);
  if isprime(q*r mod p) then count:= count+1; R:= R, p fi
od:
R;

Prog

(Python)
from sympy import nextprime, isprime
def afind(limit):
  p, q, r = 1, 2, 3
  while p < limit:
    p, q, r = q, r, nextprime(r)
    if isprime(q*r % p): print(p, end=", ")
afind(200) # Michael S. Branicky, Mar 05 2021

Crossrefs

Cf. A338566, A338570. Contained in A338577.

Sequence in context: A155189 A065384 A354217 * A340339 A126108 A100859

Adjacent sequences: A338564 A338565 A338566 * A338568 A338569 A338570

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Nov 02 2020

Status

approved