login
A352948
Primes p such that p+2, (p^2-1)/2+p and (p^2+3)/2+3*p are also prime.
2
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
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
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Apr 10 2022
STATUS
approved