A333803 - OEIS

%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