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

1,1

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

Links

Table of n, a(n) for n=1..59.

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 *)

Prog

(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
(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

Crossrefs

Cf. A000040, A035327, A050415.

Sequence in context: A190200 A162902 A026491 * A255491 A344955 A292658

Adjacent sequences: A347473 A347474 A347475 * A347477 A347478 A347479

Keyword

nonn,base

Author

Srijan Suryansh, Sep 03 2021

Extensions

More terms from Michael S. Branicky, Sep 03 2021

Status

approved