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

%I A360383 #21 Feb 22 2023 18:27:27
%S A360383 2,3,5,7,17,23,29,31,43,47,53,59,67,89,101,103,107,113,127,131,163,
%T A360383 167,173,181,191,199,233,257,269,281,317,331,353,359,367,373,379,383,
%U A360383 389,397,401,419,421,439,463,479,503,509,521,523,563,577,587,631,641,719
%N A360383 prime(k) such that (k BitOR prime(k)) is prime, where BitOR is the binary bitwise OR.
%C A360383 All Mersenne primes (A000668) belong to the sequence. - _Rémy Sigrist_, Feb 05 2023
%H A360383 Robert Israel, <a href="/A360383/b360383.txt">Table of n, a(n) for n = 1..10000</a>
%e A360383 2 is a term since k = primepi(2) = 1 and (1 BitOR 2) = 3 is a prime number.
%e A360383 101 is a term since k = primepi(101) = 26 and (26 BitOR 101) = 127 is a prime number.
%p A360383 q:= p-> andmap(isprime, [p, Bits[Or](p, numtheory[pi](p))]):
%p A360383 select(q, [$2..1000])[];  # _Alois P. Heinz_, Feb 05 2023
%t A360383 Select[Prime[Range[130]], PrimeQ[BitOr[#, PrimePi[#]]] &] (* _Amiram Eldar_, Feb 05 2023 *)
%o A360383 (PARI) { p = primes([1,719]); for (k=1, #p, if (isprime(bitor(k,p[k])), print1 (p[k]", "))) } \\ _Rémy Sigrist_, Feb 05 2023
%o A360383 (Python)
%o A360383 from sympy import isprime, primerange
%o A360383 print([p for i, p in enumerate(primerange(2, 800), 1) if isprime(i|p)]) # _Michael S. Branicky_, Feb 05 2023
%Y A360383 Cf. A000040, A000668, A000720.
%K A360383 nonn,base
%O A360383 1,1
%A A360383 _Najeem Ziauddin_, Feb 04 2023