A340408 Primes p such that p*q+q*r+r*s is prime, where q,r,s are the next primes after p.

3, 17, 19, 23, 43, 151, 157, 199, 229, 233, 331, 347, 461, 467, 491, 503, 523, 547, 563, 613, 617, 619, 653, 739, 743, 773, 941, 1021, 1031, 1051, 1063, 1097, 1103, 1117, 1163, 1193, 1237, 1259, 1279, 1373, 1429, 1489, 1523, 1553, 1601, 1609, 1613, 1627, 1663, 1709, 1733, 1907, 1999, 2011, 2087

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 06 2021

Keywords

• nonn

Examples

			a(3) = 19 is a term because 19*23+23*29+29*31 = 2003 is prime.
		

Links

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

Crossrefs

Cf. A287653.

Programs

Maple

q:= 2: r:= 3: s:= 5:
count:= 0: R:= NULL:
while count < 100 do
  p:= q; q:= r; r:= s; s:= nextprime(s);
  if isprime(p*q+q*r+r*s) then count:= count+1; R:= R, p;  fi
od:
R;

Python

from sympy import isprime, nextprime
def aupton(terms):
  p, q, r, s, alst = 2, 3, 5, 7, []
  while len(alst) < terms:
    if isprime(p*q + q*r + r*s): alst.append(p)
    p, q, r, s = q, r, s, nextprime(s)
  return alst
print(aupton(55)) # Michael S. Branicky, Mar 17 2021