A347476 Numbers which give a prime number when 0's and 1's are interchanged in their binary representation.

4, 5, 8, 10, 12, 13, 18, 20, 24, 26, 28, 29, 32, 34, 40, 44, 46, 50, 52, 56, 58, 60, 61, 66, 68, 74, 80, 84, 86, 90, 96, 98, 104, 108, 110, 114, 116, 120, 122, 124, 125, 128, 142, 146, 148, 152, 154, 158, 166, 172, 176, 182, 184, 188, 194, 196, 202, 208, 212

Offset: 1

Author

Srijan Suryansh, Sep 03 2021

Keywords

• nonn
• base

Comments

Subsequence of primes is A050415 and then, the obtained prime is always 2. We have: prime p = 2^k-3, k>=3 -> p = 11...1101_2 with a string of (k-2) digits 1 before '01' ==> 00...0010_2 = 10_2 -> 2_10. - Bernard Schott, Oct 21 2021

Crossrefs

Cf. A000040, A035327, A050415.

Programs

Maple

q:= n-> isprime(Bits[Nand](n$2)):
select(q, [$1..300])[];  # Alois P. Heinz, Sep 03 2021

Mathematica

Select[Range[200], PrimeQ @ FromDigits[IntegerDigits[#, 2] /. {0 -> 1, 1 -> 0}, 2] &] (* Amiram Eldar, Sep 03 2021 *)

PARI

isok(m) = isprime(fromdigits(apply(x->1-x, binary(m)), 2)); \\ Michel Marcus, Sep 03 2021

PARI

is(n) = isprime(1<<(logint(n, 2) + 1) - n - 1) \\ David A. Corneth, Sep 03 2021

Python

from sympy import isprime
def comp(s): z, o = ord('0'), ord('1'); return s.translate({z:o, o:z})
def ok(n): return isprime(int(comp(bin(n)[2:]), 2))
print(list(filter(ok, range(214)))) # Michael S. Branicky, Sep 03 2021

Extensions

More terms from Michael S. Branicky, Sep 03 2021