A217589 Bit reversed 16-bit numbers.

0, 32768, 16384, 49152, 8192, 40960, 24576, 57344, 4096, 36864, 20480, 53248, 12288, 45056, 28672, 61440, 2048, 34816, 18432, 51200, 10240, 43008, 26624, 59392, 6144, 38912, 22528, 55296, 14336, 47104, 30720, 63488, 1024, 33792, 17408, 50176, 9216, 41984

Offset: 0

Author

M. F. Hasler, Oct 07 2012

Keywords

• nonn
• base
• fini

Comments

The 16-bit analog of the 8-bit version A160638, see there for further links and information.

An involutive (i.e., equal to its own inverse) permutation of the numbers 0,...,65535.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A160638.

Programs

Haskell

import Data.Bits (testBit, setBit)
import Data.Word (Word16)
a217589 :: Word16 -> Word16
a217589 n = rev 0 0 where
   rev 16 y = y
   rev i y = rev (i + 1) (if testBit n i then setBit y (15 - i) else y)
-- Reinhard Zumkeller, Jan 12 2013

Maple

a:= n-> Bits[Join](ListTools[Reverse](Bits[Split](n, bits=16))):
seq(a(n), n=0..37);  # Alois P. Heinz, Nov 28 2024

Mathematica

Table[FromDigits[Reverse[IntegerDigits[n, 2, 16]], 2], {n, 0, 50}] (* T. D. Noe, Oct 09 2012 *)
IntegerReverse[Range[0, 127], 2, 16] (* Paolo Xausa, Nov 28 2024 *)

PARI

a(n)=sum(i=0,15,bittest(n,15-i)<
				

Formula

a(a(n))=n.

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.

a(n) is even for all n < 2^15 = a(1) and odd for all larger n.

a(n) = floor(A030101(n+65536)/2). - Reinhard Zumkeller, Jan 12 2013