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A337491 Numbers k such that exactly one of 2*k + 3 and 4*k + 3 is prime.

%I A337491 #13 Jan 26 2023 18:56:25
%S A337491 8,11,13,16,22,26,28,29,31,35,37,38,41,43,44,50,53,56,59,64,65,68,70,
%T A337491 73,74,76,80,85,86,88,91,97,98,107,109,112,113,116,118,121,122,125,
%U A337491 127,133,134,136,137,139,142,145,146,149,151,152,155,160,161,167,170
%N A337491 Numbers k such that exactly one of 2*k + 3 and 4*k + 3 is prime.
%C A337491 Integers that are in A067076 or in A095278, but not in both. - _Michel Marcus_, Aug 29 2020
%H A337491 K. D. Bajpai, <a href="/A337491/b337491.txt">Table of n, a(n) for n = 1..5000</a>
%e A337491 a(1) = 8 is a term because 2*8 + 3 = 19 is a prime; but 4*8 + 3 = 35 = (5*7) is a composite number.
%e A337491 a(4) = 16 is a term because 2*16 + 3 = 35 = (5*7) is a composite number; but 4*16 + 3 = 67  is a prime.
%e A337491 a(6) = 26 is a term because 2*26 + 3 = 55 = (5*11) is a composite number; but 4*26 + 3 = 107  is a prime.
%p A337491 A337491:=n->`if`((isprime(2*n+3) xor isprime(4*n+3)), n, NULL): seq(A337491(n), n=1..500);
%t A337491 Select[Range[0, 250], Xor[PrimeQ[2 # + 3], PrimeQ[4 # + 3]] &]
%t A337491 Select[Range[200],Total[Boole[PrimeQ[{2,4}#+3]]]==1&] (* _Harvey P. Dale_, Jan 26 2023 *)
%o A337491 (PARI) isok(k) = bitxor(isprime(2*k+3), isprime(4*k+3)); \\ _Michel Marcus_, Aug 29 2020
%Y A337491 Cf. A063908, A067076, A095278, A337480.
%K A337491 nonn
%O A337491 1,1
%A A337491 _K. D. Bajpai_, Aug 29 2020