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A236688 Primes p such that prime(p^2) + 2 is also prime.

%I A236688 #14 Aug 29 2021 11:13:35
%S A236688 7,53,83,107,149,223,367,509,701,769,853,971,1039,1229,1283,1327,1373,
%T A236688 1381,1439,1447,1459,1783,1873,1973,2237,2243,2269,2339,2347,2437,
%U A236688 2459,2521,2531,2797,2857,3001,3391,3413,3461,3583,3593,3631,3659,3769,3889,3947
%N A236688 Primes p such that prime(p^2) + 2 is also prime.
%H A236688 K. D. Bajpai, <a href="/A236688/b236688.txt">Table of n, a(n) for n = 1..1119</a>
%e A236688 7 is prime and appears in the sequence: prime(7^2) = 227 and 227+2 = 229, which is also prime.
%e A236688 53 is prime and appears in the sequence: prime(53^2) = 25469 and 25469+2 = 25471, which is also prime.
%p A236688 KD := proc() local a,b; a:=ithprime(n); b:=ithprime(a^2)+2; if isprime (b) then RETURN (a);fi; end: seq(KD(), n=1..700);
%t A236688 Select[Prime[Range[600]],PrimeQ[Prime[#^2]+2]&] (* _Harvey P. Dale_, Aug 29 2021 *)
%o A236688 (PARI)
%o A236688 default(primelimit,2^31)
%o A236688 s=[]; forprime(p=2, 4000, if(isprime(prime(p^2)+2), s=concat(s, p))); s \\ _Colin Barker_, Jan 30 2014
%Y A236688 Cf. A000040, A234695, A236119.
%K A236688 nonn
%O A236688 1,1
%A A236688 _K. D. Bajpai_, Jan 29 2014