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

0,2

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

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

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 *)

Prog

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

Crossrefs

Cf. A160638.

Sequence in context: A289478 A222528 A232393 * A069276 A195235 A223335

Adjacent sequences: A217586 A217587 A217588 * A217590 A217591 A217592

Keyword

nonn,base,fini

Author

M. F. Hasler, Oct 07 2012

Status

approved