

A057889


Bitreverse of n, including as many leading as trailing zeros.


37



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
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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 xrange(101)] # Indranil Ghosh, Jun 11 2017


CROSSREFS

Cf. A030101, A000265, A006519, A006995, A057890, A057891.
Sequence in context: A033621 A108548 A322464 * A235027 A325402 A110029
Adjacent sequences: A057886 A057887 A057888 * A057890 A057891 A057892


KEYWORD

easy,nonn,base,look


AUTHOR

Marc LeBrun, Sep 25 2000


STATUS

approved



