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A356510 Primes p such that 2*p^2 - 7, 2*p^2 - 1, and 2*p^2 + 3 are prime.

%I A356510 #14 Sep 05 2022 12:43:16
%S A356510 43,127,197,3613,3767,4957,28687,29723,40193,46817,66403,78737,89137,
%T A356510 93253,104243,105337,105673,110543,114113,123397,127247,145963,148303,
%U A356510 168713,173293,190387,201893,207367,213613,241597,256117,261323,268253,278543,283807,333227,339373,340913,356173,359143
%N A356510 Primes p such that 2*p^2 - 7, 2*p^2 - 1, and 2*p^2 + 3 are prime.
%C A356510 All terms == 3 or 7 (mod 10).
%C A356510 All terms == 1 or 13 (mod 14). - _Jon E. Schoenfield_, Sep 05 2022
%H A356510 Robert Israel, <a href="/A356510/b356510.txt">Table of n, a(n) for n = 1..1000</a>
%e A356510 a(3) = 197 is a term because 197, 2*197^2 - 7 = 77611, 2*197^2 - 1 = 77617, and 2*197^2 + 3 = 77621 are all prime.
%p A356510 filter:= p -> isprime(p) and isprime(2*p^2+3) and isprime(2*p^2-1) and isprime(2*p^2-7):
%p A356510 select(filter, [seq(i,i=3..1000000,2)]);
%t A356510 Select[Prime[Range[30000]], AllTrue[2*#^2 + {-7, -1, 3}, PrimeQ] &] (* _Amiram Eldar_, Aug 09 2022 *)
%o A356510 (Python)
%o A356510 from sympy import isprime
%o A356510 def ok(n): return isprime(n) and all(isprime(2*n*n-i) for i in [7, 1, -3])
%o A356510 print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Aug 09 2022
%Y A356510 Contained in A106483 and A243595.
%K A356510 nonn
%O A356510 1,1
%A A356510 _J. M. Bergot_ and _Robert Israel_, Aug 09 2022