A360383 prime(k) such that (k BitOR prime(k)) is prime, where BitOR is the binary bitwise OR.

2, 3, 5, 7, 17, 23, 29, 31, 43, 47, 53, 59, 67, 89, 101, 103, 107, 113, 127, 131, 163, 167, 173, 181, 191, 199, 233, 257, 269, 281, 317, 331, 353, 359, 367, 373, 379, 383, 389, 397, 401, 419, 421, 439, 463, 479, 503, 509, 521, 523, 563, 577, 587, 631, 641, 719

Offset: 1

Author

Najeem Ziauddin, Feb 04 2023

Keywords

• nonn
• base

Comments

All Mersenne primes (A000668) belong to the sequence. - Rémy Sigrist, Feb 05 2023

Examples

			2 is a term since k = primepi(2) = 1 and (1 BitOR 2) = 3 is a prime number.
101 is a term since k = primepi(101) = 26 and (26 BitOR 101) = 127 is a prime number.
		

Links

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

Crossrefs

Cf. A000040, A000668, A000720.

Programs

Maple

q:= p-> andmap(isprime, [p, Bits[Or](p, numtheory[pi](p))]):
select(q, [$2..1000])[];  # Alois P. Heinz, Feb 05 2023

Mathematica

Select[Prime[Range[130]], PrimeQ[BitOr[#, PrimePi[#]]] &] (* Amiram Eldar, Feb 05 2023 *)

PARI

{ p = primes([1,719]); for (k=1, #p, if (isprime(bitor(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, 800), 1) if isprime(i|p)]) # Michael S. Branicky, Feb 05 2023