A160638 -id:A160638 - cp's OEIS frontend

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

M. F. Hasler, Oct 07 2012

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.

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

Cf. A160638.

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

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

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)<
				
```

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

A217557 The difference between the reversal of an 8-bit integer and the original integer.

Original entry on oeis.org

0, 127, 62, 189, 28, 155, 90, 217, 8, 135, 70, 197, 36, 163, 98, 225, -8, 119, 54, 181, 20, 147, 82, 209, 0, 127, 62, 189, 28, 155, 90, 217, -28, 99, 34, 161, 0, 127, 62, 189, -20, 107, 42, 169, 8, 135, 70, 197, -36, 91, 26, 153, -8, 119, 54, 181, -28, 99

Offset: 0

Jon Perry, Oct 06 2012

The difference between the reversal of an 8-bit integer and the original integer.

			5 -> 00000101 -> 10100000 = 160 so a(5) = 155.

Vincenzo Librandi, Table of n, a(n) for n = 0..255 (all terms of the sequence).

Cf. A160638.

Table[FromDigits[Reverse[PadLeft[IntegerDigits[n,2],8,0]],2]-n,{n,0,60}] (* Harvey P. Dale, Oct 12 2012 *)

A217557(n)=sum(i=0,7,bittest(n,7-i)<M. F. Hasler, Oct 07 2012

a(n) = A160638(n) - n.

cp's OEIS Frontend

A217589 Bit reversed 16-bit numbers.

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