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

1,1

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000040, A000720.

Sequence in context: A275491 A360673 A183435 * A141777 A297883 A215206

Adjacent sequences: A360382 A360383 A360384 * A360386 A360387 A360388

Keyword

nonn,base

Author

Najeem Ziauddin, Feb 05 2023

Status

approved