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

2, 7, 13, 29, 37, 43, 53, 61, 71, 79, 101, 131, 151, 199, 223, 281, 293, 317, 337, 349, 383, 409, 421, 457, 521, 557, 569, 641, 683, 733, 911, 983, 1013, 1049, 1151, 1223, 1249, 1373, 1429, 1511, 1531, 1721, 1747, 1759, 1789, 1831, 1931, 2017, 2029, 2213, 2311

Offset: 1

Author

Najeem Ziauddin, Feb 05 2023

Keywords

• nonn
• base

Examples

			2 is a term since k = primepi(2) = 1 and (1 BitXOR 2) = 3 is a prime number.
151 is a term since k = primepi(151) = 36 and (36 BitXOR 151) = 179 is a prime number.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000720.

Programs

Maple

q:= p-> andmap(isprime, [p, Bits[Xor](p, numtheory[pi](p))]):
select(q, [$2..3000])[];  # Alois P. Heinz, Feb 05 2023

Mathematica

Select[Prime[Range[400]], PrimeQ[BitXor[#, PrimePi[#]]] &] (* Amiram Eldar, Feb 05 2023 *)

PARI

{ p = primes([1,2311]); for (k=1, #p, if (isprime(bitxor(k,p[k])), print1 (p[k]", "))) } \\ Rémy Sigrist, Feb 05 2023

Python

from sympy import isprime, primerange
print([p for i, p in enumerate(primerange(2, 10**4), 1) if isprime(i^p)]) # Michael S. Branicky, Feb 05 2023