cp's OEIS Frontend

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

%I A352948 #15 Apr 20 2022 00:07:15
%S A352948 5,29,599,2687,3557,4337,5009,8597,23687,26249,26699,36527,37307,
%T A352948 39509,55049,59669,61559,65519,69497,72269,72869,74507,75209,81017,
%U A352948 82559,87557,92639,93479,97157,102407,103289,106217,114689,120917,136067,140627,147449,156797,162749,167117,179999,181397
%N A352948 Primes p such that p+2, (p^2-1)/2+p and (p^2+3)/2+3*p are also prime.
%C A352948 Lower twin primes p such that if q = p+2, (p*q-1)/2 and (p*q-1)/2+p+q are also prime.
%H A352948 Robert Israel, <a href="/A352948/b352948.txt">Table of n, a(n) for n = 1..10000</a>
%e A352948 a(3) = 599 is a term because it, 599+2 = 601, (599*601-1)/2 = 179999, and 179999+599+601 = 181199 are prime.
%t A352948 Select[Range[200000], And @@ PrimeQ[{#, # + 2, (#^2 - 1)/2 + # , (#^2 + 3)/2 + 3*#}] &] (* _Amiram Eldar_, Apr 10 2022 *)
%o A352948 (Python)
%o A352948 from itertools import islice
%o A352948 from sympy import isprime, nextprime
%o A352948 def agen(): # generator of terms
%o A352948     p, q = 3, 5
%o A352948     while True:
%o A352948         if q == p+2 and isprime((p*q-1)//2) and isprime((p*q-1)//2+p+q):
%o A352948             yield p
%o A352948         p, q = q, nextprime(q)
%o A352948 print(list(islice(agen(), 42))) # _Michael S. Branicky_, Apr 10 2022
%Y A352948 Subset of A109945.
%Y A352948 Cf. A001359.
%K A352948 nonn
%O A352948 1,1
%A A352948 _J. M. Bergot_ and _Robert Israel_, Apr 10 2022