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%I #11 Sep 15 2021 17:15:11
%S 2,3,5,233,653,683,1013,1973,2003,2393,2543,2753,3023,3413,5003,5333,
%T 7043,7823,8663,9293,10613,13463,13913,14783,15233,15923,16823,18233,
%U 20693,20753,21713,21803,22433,27743,27983,29723,30323,30773,31253,31793,32003,33053,33623,33773,34283,36083,37013
%N Primes p such that 2*p+1 and 4*p^2+1 are also prime.
%C The generalized Bunyakovsky conjecture implies there are infinitely many terms.
%H Robert Israel, <a href="/A333803/b333803.txt">Table of n, a(n) for n = 1..10000</a>
%H Mathematics StackExchange,<a href="https://math.stackexchange.com/questions/3610974/find-all-p-such-that-p-2p1-4p21-are-prime/3610993">Find all p such that p, 2p+1, 4p^2+1 are prime</a>
%e a(3)=5 is a member because 5, 2*5+1=11 and 4*5^2+1= 101 are all prime.
%p filter:= proc(n)
%p isprime(n) and isprime(2*n+1) and isprime(4*n^2+1)
%p end proc:
%p select(filter, [2,3,seq(i,i=5..10^5,6)]);
%t Select[Prime[Range[4000]],AllTrue[{2#+1,4#^2+1},PrimeQ]&] (* _Harvey P. Dale_, Sep 15 2021 *)
%Y Intersection of A005384 and A052291.
%K nonn
%O 1,1
%A _Robert Israel_, Apr 05 2020
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