%I #11 Apr 06 2022 10:37:14

%S 2,3,43,47,107,139,191,211,223,239,293,313,337,541,743,757,863,1013,

%T 1153,1231,1619,2113,2137,2287,2297,2423,2543,2729,2749,2897,3079,

%U 3089,3313,3863,3947,4241,4271,4583,4649,4993,5581,6571,6637,6911,7547,8629,8849,8867,9049,9661

%N Primes p with p^2 - 2 and prime(p)^2 - 2 both prime.

%C According to the conjecture in A237413, this sequence should have infinitely many terms.

%H Zhi-Wei Sun, <a href="/A237414/b237414.txt">Table of n, a(n) for n = 1..10000</a>

%H Z.-W. Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641, 2014

%e a(1) = 2 since 2^2 - 2 = 2 and prime(2)^2 - 2 = 3^2 - 2 = 7 are both prime.

%t p[n_]:=PrimeQ[n^2-2]

%t n=0;Do[If[p[Prime[k]]&&p[Prime[Prime[k]]],n=n+1;Print[n," ",Prime[k]]],{k,1,1000}]

%t Select[Prime[Range[1200]],AllTrue[{#^2-2,Prime[#]^2-2},PrimeQ]&] (* _Harvey P. Dale_, Apr 06 2022 *)

%Y Cf. A000040, A049002, A062326, A230502, A237413.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Feb 07 2014