A204232 Numbers whose binary reversal is prime.

3, 5, 6, 7, 10, 11, 12, 13, 14, 17, 20, 22, 23, 24, 25, 26, 28, 29, 31, 34, 37, 40, 41, 43, 44, 46, 47, 48, 50, 52, 53, 55, 56, 58, 61, 62, 67, 68, 71, 73, 74, 77, 80, 82, 83, 86, 88, 91, 92, 94, 96, 97, 100, 101, 104, 106, 107, 110, 112, 113, 115, 116, 121

Offset

1,1

Comments

Base-2 analog of A095179.

If k is a term, then 2*k is a term too. - Michel Marcus, Apr 19 2020

Links

Michel Marcus, Table of n, a(n) for n = 1..1000

Example

3, 5 and 7 are in the sequence because their binary reversal, equal to themselves, is prime.
a(3)=6 is in the sequence, because 6=110[2] (written in base 2), whose reversal 011[2]=3 is prime.
a(5)=11 is in the sequence, because 11=1011[2] (written in base 2), whose reversal 1101[2]=13 is prime.

Mathematica

Select[Range[170], PrimeQ[FromDigits[Reverse[IntegerDigits[#, 2]], 2]] &] (* Alonso del Arte, Jan 13 2012 *)

Prog

(PARI) for(n=1, 1e2, isprime((t=binary(n))*vector(#t, i, 1<<i)~\2) & print1(n", "))
(Python)
from sympy import isprime
def ok(n): return isprime(int(bin(n)[2:][::-1], 2))
print(list(filter(ok, range(1, 122)))) # Michael S. Branicky, Sep 06 2021
(Python) # alternate program constructing terms directly from primes
from sympy import isprime, primerange
def auptobits(maxbits):
    alst = []
    for p in primerange(3, 1<<maxbits):
        b = bin(p)[2:]; br = b[::-1]; t = int(br, 2)
        alst.extend(t<<i for i in range(maxbits-len(br)+1))
    return sorted(alst)
print(auptobits(7)) # Michael S. Branicky, Oct 29 2024

Crossrefs

Cf. A030101, A095179.

Positions of 2's in A227864.

Sequence in context: A352826 A335657 A038550 * A028730 A028747 A136806

Adjacent sequences: A204229 A204230 A204231 * A204233 A204234 A204235

Keyword

nonn,base,easy

Author

M. F. Hasler, Jan 13 2012

Status

approved