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A192794 Numbers k such that k + 2 and k^2 + 4 are primes.

%I A192794 #34 Nov 12 2023 02:53:10
%S A192794 1,3,5,15,17,27,35,45,57,65,87,95,125,135,137,147,155,177,255,267,275,
%T A192794 347,357,407,447,455,477,507,605,615,707,717,755,767,785,795,827,837,
%U A192794 905,935,945,1185,1235,1247,1257,1275,1325,1365,1457,1497,1595,1695
%N A192794 Numbers k such that k + 2 and k^2 + 4 are primes.
%C A192794 a(n) is odd for all n. For n > 2, the last digit of a(n) is either 5 or 7 because for n == 1, 3, 9 mod 10, either n+2 == 5 (mod 10) or n^2+4 == 5 (mod 10). Thus if m>1 is a term, then m+2 is in A045378. - _Chai Wah Wu_, Sep 06 2020
%H A192794 Robert Israel, <a href="/A192794/b192794.txt">Table of n, a(n) for n = 1..10000</a>
%e A192794 1 + 2 = 3 and  1 + 4 = 5 are primes,
%e A192794 3 + 2 = 5 and  9 + 4 = 13 are primes,
%e A192794 5 + 2 = 7 and 25 + 4 = 29 are primes.
%p A192794 filter:= n -> isprime(n+2) and isprime(n^2+4):
%p A192794 select(filter, [seq(i,i=1..2000,2)]); # _Robert Israel_, Nov 11 2023
%o A192794 (PARI) {a=2;forstep(n=1,2000,2,if(isprime(n+a)&&isprime(n^2+a^2), print1(n",")))}
%Y A192794 Cf. A045378, A070689.
%K A192794 nonn
%O A192794 1,2
%A A192794 _Zak Seidov_, Dec 19 2012