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

1,1

Comments

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000040, A000668, A000720.

Sequence in context: A286499 A116947 A066277 * A164134 A152184 A135948

Adjacent sequences: A360380 A360381 A360382 * A360384 A360385 A360386

Keyword

nonn,base

Author

Najeem Ziauddin, Feb 04 2023

Status

approved