A342504 Primes p such that (p*r+q*s)/2 is prime, where p,q,r,s are consecutive primes.

5, 7, 37, 53, 79, 97, 107, 109, 263, 293, 409, 463, 563, 571, 701, 853, 877, 1031, 1423, 1567, 1699, 1747, 1789, 2029, 2837, 2917, 2969, 3137, 3251, 3331, 3413, 3461, 3533, 3881, 3889, 4229, 4513, 4909, 4937, 5051, 5059, 5843, 6011, 6151, 6361, 6521, 6779, 7331, 7547, 7673, 8243, 8269, 8287, 8693

Offset

1,1

Links

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

Example

a(3) = 37 is a term because 37,41,43,47 are consecutive primes and (37*43+41*47)/2 = 1759 is prime.

Maple

R:= NULL: count:= 0:
q:= 3: r:= 5: s:= 7:
while count < 100 do
  p:= q; q:= r; r:= s; s:= nextprime(s);
  if isprime((p*r+q*s)/2) then
     count:= count+1; R:= R, p;
  fi
od:
R;

Prog

(Python)
from sympy import isprime, nextprime
def aupton(terms):
  alst, p, q, r, s = [], 2, 3, 5, 7
  while len(alst) < terms:
    if isprime((p*r + q*s)//2): alst.append(p)
    p, q, r, s = q, r, s, nextprime(s)
  return alst
print(aupton(54)) # Michael S. Branicky, Mar 14 2021

Crossrefs

Cf. A342505, A342506.

Sequence in context: A196203 A196473 A081851 * A192156 A322380 A006067

Adjacent sequences: A342501 A342502 A342503 * A342505 A342506 A342507

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Mar 14 2021

Status

approved