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A337480 Numbers k such that exactly one of 6*k + 5 and 12*k + 5 is prime.

%I A337480 #8 Sep 01 2020 11:40:37
%S A337480 6,12,13,17,18,19,23,26,27,28,31,33,39,41,44,47,48,49,52,53,54,56,57,
%T A337480 59,67,68,69,74,76,78,83,86,87,88,91,93,94,97,101,109,112,114,116,117,
%U A337480 124,126,128,129,132,133,137,139,141,144,146,147,151,154,159,161
%N A337480 Numbers k such that exactly one of 6*k + 5 and 12*k + 5 is prime.
%H A337480 K. D. Bajpai, <a href="/A337480/b337480.txt">Table of n, a(n) for n = 1..10000</a>
%e A337480 a(5) = 18 is a term because 6*18 + 5 = 113 is prime; but 12*18 + 5 = 221 = (13*17) is a composite number.
%e A337480 a(8) = 26 is a term because 6*26 + 5 = 161 = (7*23) is a composite number; but 12*26 + 5 = 317 is prime.
%p A337480 A337480:=k->`if`(isprime(6*k+5) xor isprime(12*k+5),k, NULL): seq(A337480(k), k=1..1000);
%t A337480 Select[Range[0, 250], Xor[PrimeQ[6 # + 5], PrimeQ[12 # + 5]] &]
%o A337480 (PARI) for(k=1, 1000, if (bitxor(isprime(6*k+5), isprime(12*k+5)), print1(k, ", ")));
%Y A337480 Cf. A063913, A145487, A145490, A172287.
%K A337480 nonn
%O A337480 1,1
%A A337480 _K. D. Bajpai_, Aug 28 2020