%I #13 Jan 23 2018 06:43:17
%S 0,32768,16384,49152,8192,40960,24576,57344,4096,36864,20480,53248,
%T 12288,45056,28672,61440,2048,34816,18432,51200,10240,43008,26624,
%U 59392,6144,38912,22528,55296,14336,47104,30720,63488,1024,33792,17408,50176,9216,41984
%N Bit reversed 16-bit numbers.
%C The 16-bit analog of the 8-bit version A160638, see there for further links and information.
%C An involutive (i.e., equal to its own inverse) permutation of the numbers 0,...,65535.
%H Vincenzo Librandi, <a href="/A217589/b217589.txt">Table of n, a(n) for n = 0..10000</a>
%F a(a(n))=n.
%F a(m)+a(n)=a(m+n) whenever n & m = 0, where "&" is binary bit-AND, i.e., whenever m and n have no (1-)bits in common.
%F a(n) is even for all n < 2^15 = a(1) and odd for all larger n.
%F a(n) = floor(A030101(n+65536)/2). - _Reinhard Zumkeller_, Jan 12 2013
%t Table[FromDigits[Reverse[IntegerDigits[n, 2, 16]], 2], {n, 0, 50}] (* _T. D. Noe_, Oct 09 2012 *)
%o (PARI) a(n)=sum(i=0,15,bittest(n,15-i)<<i)
%o (Haskell)
%o import Data.Bits (testBit, setBit)
%o import Data.Word (Word16)
%o a217589 :: Word16 -> Word16
%o a217589 n = rev 0 0 where
%o rev 16 y = y
%o rev i y = rev (i + 1) (if testBit n i then setBit y (15 - i) else y)
%o -- _Reinhard Zumkeller_, Jan 12 2013
%K nonn,base,fini
%O 0,2
%A _M. F. Hasler_, Oct 07 2012