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A351528
Prime numbers ordered by their binary reversal.
1
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
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Feb 13 2022
STATUS
approved