A352948 Primes p such that p+2, (p^2-1)/2+p and (p^2+3)/2+3*p are also prime.

5, 29, 599, 2687, 3557, 4337, 5009, 8597, 23687, 26249, 26699, 36527, 37307, 39509, 55049, 59669, 61559, 65519, 69497, 72269, 72869, 74507, 75209, 81017, 82559, 87557, 92639, 93479, 97157, 102407, 103289, 106217, 114689, 120917, 136067, 140627, 147449, 156797, 162749, 167117, 179999, 181397

Offset

1,1

Comments

Lower twin primes p such that if q = p+2, (p*q-1)/2 and (p*q-1)/2+p+q are also prime.

Links

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

Example

a(3) = 599 is a term because it, 599+2 = 601, (599*601-1)/2 = 179999, and 179999+599+601 = 181199 are prime.

Mathematica

Select[Range[200000], And @@ PrimeQ[{#, # + 2, (#^2 - 1)/2 + # , (#^2 + 3)/2 + 3*#}] &] (* Amiram Eldar, Apr 10 2022 *)

Prog

(Python)
from itertools import islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    p, q = 3, 5
    while True:
        if q == p+2 and isprime((p*q-1)//2) and isprime((p*q-1)//2+p+q):
            yield p
        p, q = q, nextprime(q)
print(list(islice(agen(), 42))) # Michael S. Branicky, Apr 10 2022

Crossrefs

Subset of A109945.

Cf. A001359.

Sequence in context: A197962 A259534 A176680 * A352951 A069142 A144994

Adjacent sequences: A352945 A352946 A352947 * A352949 A352950 A352951

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Apr 10 2022

Status

approved