login
Numbers k such that exactly one of 6*k + 5 and 12*k + 5 is prime.
2

%I #8 Sep 01 2020 11:40:37

%S 6,12,13,17,18,19,23,26,27,28,31,33,39,41,44,47,48,49,52,53,54,56,57,

%T 59,67,68,69,74,76,78,83,86,87,88,91,93,94,97,101,109,112,114,116,117,

%U 124,126,128,129,132,133,137,139,141,144,146,147,151,154,159,161

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

%H K. D. Bajpai, <a href="/A337480/b337480.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 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:=k->`if`(isprime(6*k+5) xor isprime(12*k+5),k, NULL): seq(A337480(k), k=1..1000);

%t Select[Range[0, 250], Xor[PrimeQ[6 # + 5], PrimeQ[12 # + 5]] &]

%o (PARI) for(k=1, 1000, if (bitxor(isprime(6*k+5), isprime(12*k+5)), print1(k, ", ")));

%Y Cf. A063913, A145487, A145490, A172287.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Aug 28 2020