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A360385 prime(k) such that (k BitXOR prime(k)) is prime, where BitXOR is the binary bitwise XOR.

%I A360385 #17 Feb 23 2023 02:00:17
%S A360385 2,7,13,29,37,43,53,61,71,79,101,131,151,199,223,281,293,317,337,349,
%T A360385 383,409,421,457,521,557,569,641,683,733,911,983,1013,1049,1151,1223,
%U A360385 1249,1373,1429,1511,1531,1721,1747,1759,1789,1831,1931,2017,2029,2213,2311
%N A360385 prime(k) such that (k BitXOR prime(k)) is prime, where BitXOR is the binary bitwise XOR.
%H A360385 Robert Israel, <a href="/A360385/b360385.txt">Table of n, a(n) for n = 1..10000</a>
%e A360385 2 is a term since k = primepi(2) = 1 and (1 BitXOR 2) = 3 is a prime number.
%e A360385 151 is a term since k = primepi(151) = 36 and (36 BitXOR 151) = 179 is a prime number.
%p A360385 q:= p-> andmap(isprime, [p, Bits[Xor](p, numtheory[pi](p))]):
%p A360385 select(q, [$2..3000])[];  # _Alois P. Heinz_, Feb 05 2023
%t A360385 Select[Prime[Range[400]], PrimeQ[BitXor[#, PrimePi[#]]] &] (* _Amiram Eldar_, Feb 05 2023 *)
%o A360385 (PARI) { p = primes([1,2311]); for (k=1, #p, if (isprime(bitxor(k,p[k])), print1 (p[k]", "))) } \\ _Rémy Sigrist_, Feb 05 2023
%o A360385 (Python)
%o A360385 from sympy import isprime, primerange
%o A360385 print([p for i, p in enumerate(primerange(2, 10**4), 1) if isprime(i^p)]) # _Michael S. Branicky_, Feb 05 2023
%Y A360385 Cf. A000040, A000720.
%K A360385 nonn,base
%O A360385 1,1
%A A360385 _Najeem Ziauddin_, Feb 05 2023