A057889 Bit-reverse of n, including as many leading as trailing zeros.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 12, 11, 14, 15, 16, 17, 18, 25, 20, 21, 26, 29, 24, 19, 22, 27, 28, 23, 30, 31, 32, 33, 34, 49, 36, 41, 50, 57, 40, 37, 42, 53, 52, 45, 58, 61, 48, 35, 38, 51, 44, 43, 54, 59, 56, 39, 46, 55, 60, 47, 62, 63, 64, 65, 66, 97, 68, 81, 98, 113

Offset

0,3

Comments

In other words, keep the trailing zeros in the binary expansion of n fixed, but reverse all the digits up to that point. - N. J. A. Sloane, May 30 2016

A permutation of integers consisting only of fixed points and pairs. a(n)=n when n is a binary palindrome (including as many leading as trailing zeros), otherwise a(n)=A003010(n) (i.e. n has no axis of symmetry). A057890 gives the palindromes (fixed points, akin to A006995) while A057891 gives the "antidromes" (pairs).

Links

N. J. A. Sloane, Table of n, a(n) for n = 0..16384, May 30 2016 [First 8192 terms from Ivan Neretin, Jul 09 2015]

Formula

a(n) = A030101(A000265(n)) * A006519(n), with a(0)=0.

Example

a(6)=6 because 0110 is a palindrome, but a(11)=13 because 1011 reverses into 1101.

Mathematica

Table[FromDigits[Reverse[IntegerDigits[n, 2]], 2]*2^IntegerExponent[n, 2], {n, 71}] (* Ivan Neretin, Jul 09 2015 *)

Prog

(Python)
def a(n):
    x = bin(n)[2:]
    y = x[::-1]
    return int(str(int(y))+(len(x) - len(str(int(y))))*'0', 2)
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 11 2017

Crossrefs

Cf. A030101, A000265, A006519, A006995, A057890, A057891.

Sequence in context: A333692 A333693 A322464 * A235027 A337304 A325402

Adjacent sequences: A057886 A057887 A057888 * A057890 A057891 A057892

Keyword

easy,nonn,base,look

Author

Marc LeBrun, Sep 25 2000

Status

approved