A351528 Prime numbers ordered by their binary reversal.

2, 3, 5, 7, 13, 11, 17, 29, 19, 23, 31, 41, 37, 53, 61, 43, 59, 47, 97, 113, 73, 89, 101, 109, 67, 83, 107, 71, 103, 79, 127, 193, 241, 137, 233, 197, 229, 149, 181, 173, 157, 131, 163, 227, 211, 179, 139, 251, 199, 167, 151, 239, 223, 191, 257, 449, 353, 401

Offset

1,1

Comments

See A104154 for the base-10 variant.

Mersenne primes (A000668) and Fermat primes (A019434) appear at their natural position.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..6542

Example

The first terms, alongside their binary and reverse binary expansions, are:
  n   a(n)  bin(a(n))  bin(rev(a(n)))
  --  ----  ---------  --------------
   1     2         10               1
   2     3         11              11
   3     5        101             101
   4     7        111             111
   5    13       1101            1011
   6    11       1011            1101
   7    17      10001           10001
   8    29      11101           10111
   9    19      10011           11001
  10    23      10111           11101
  11    31      11111           11111

Mathematica

SortBy[Select[Range[2^9], PrimeQ], IntegerReverse[#, 2] &] (* Amiram Eldar, Feb 15 2022 *)

Prog

(PARI) rev(n) = fromdigits(Vecrev(binary(n)), 2)
print (vecsort(primes([1, 2^9]), (p, q)->rev(p)-rev(q))[1..58])
(Python)
from itertools import count, islice
from sympy import primerange
def A351528_gen(): # generator of terms
    yield from (int(d[::-1], 2) for l in count(1) for d in sorted(bin(m)[:1:-1] for m in primerange(2**(l-1), 2**l)))
A351528_list = list(islice(A351528_gen(), 20)) # Chai Wah Wu, Feb 17 2022

Crossrefs

Cf. A000668, A019434, A030101, A098957, A104154.

Sequence in context: A108546 A065107 A338944 * A185956 A316885 A225039

Adjacent sequences: A351525 A351526 A351527 * A351529 A351530 A351531

Keyword

nonn,base

Author

Rémy Sigrist, Feb 13 2022

Status

approved