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

1,1

Links

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

Example

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

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;

Prog

(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

Crossrefs

Cf. A287653.

Sequence in context: A101144 A038886 A019342 * A339544 A029473 A103088

Adjacent sequences: A340405 A340406 A340407 * A340409 A340410 A340411

Keyword

nonn

Author

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

Status

approved