A343449 Primes of the form p+q*(r+s), where p,q,r,s are consecutive primes.

173, 337, 479, 727, 1399, 2447, 3727, 10859, 11897, 22349, 23857, 26267, 80963, 105097, 112069, 170081, 191861, 243931, 276343, 284593, 613181, 665213, 771863, 827521, 862607, 951413, 1050449, 1158961, 1334093, 1380259, 1435519, 1495517, 1584983, 1660697, 1745581, 1847861, 1929569, 2067529

Offset

1,1

Comments

a(n) = p+q*(r+s) where p = A343448(n) and q,r,s are the next three primes after p.

Links

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

Example

For n = 3, A343448(3) = 11 and the next three primes are 13, 17, 19, so a(3) = 11+13*(17+19) = 479.

Maple

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

Prog

(Python)
from sympy import isprime, nextprime
def aupto(limit):
  p, q, r, s, alst = 2, 3, 5, 7, []
  t = p + q*(r+s)
  while t <= limit:
    if isprime(t): alst.append(t)
    p, q, r, s = q, r, s, nextprime(s)
    t = p + q*(r+s)
  return alst
print(aupto(2067529)) # Michael S. Branicky, Apr 15 2021

Crossrefs

Cf. A343448.

Sequence in context: A241045 A241046 A142206 * A142004 A047986 A096703

Adjacent sequences: A343446 A343447 A343448 * A343450 A343451 A343452

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Apr 15 2021

Status

approved