A160638 Bit-reversed 8-bit binary numbers.

0, 128, 64, 192, 32, 160, 96, 224, 16, 144, 80, 208, 48, 176, 112, 240, 8, 136, 72, 200, 40, 168, 104, 232, 24, 152, 88, 216, 56, 184, 120, 248, 4, 132, 68, 196, 36, 164, 100, 228, 20, 148, 84, 212, 52, 180, 116, 244, 12, 140, 76, 204, 44, 172, 108, 236, 28, 156

Offset: 0

Author

Russ Cox, May 21 2009

Keywords

• base
• easy
• fini
• full
• nonn
• nice

Comments

This sequence is found in computer programs that need to reverse the bits in a byte, typically during data compression or other bit-level encoding. a(n) is its own inverse: a(a(n)) = n.

A permutation of the integers 0-255. - Jon Perry, Oct 06 2012

a(n) is even for 0 <= n< 128 and odd for n <= 128 < 256. - Jon Perry, Oct 06 2012

a(m) + a(n) = a(m+n) when the binary representations of m and n have no bits in common. - Jon Perry, Oct 06 2012

Examples

			n = 1 = 00000001 binary, so a(1) = 10000000 binary = 128.
n = 29 = 00011101 binary, so a(29) = 10111000 binary = 184.
		

References

• Henry S. Warren, Hacker's Delight, Addison-Wesley, 2002, pages 101-106.

Links

• Russ Cox, Table of n, a(n) for n = 0 .. 255 (full sequence)
• Sean Anderson, Bit Twiddling Hacks
• Michael Beeler, R. William Gosper and Richard C. Schroeppel, HAKMEM (MIT AI Memo 239, Feb. 29, 1972), Item 167.

Crossrefs

Cf. A217589.

Programs

C

int a = 0; for(int i=0; i<8; i++) if(n & (1<
				

Haskell

import Data.Bits (testBit, setBit)
import Data.Word (Word8)
a160638 :: Word8 -> Word8
a160638 n = rev 0 0 where
   rev 8 y = y
   rev i y = rev (i + 1) (if testBit n i then setBit y (7 - i) else y)
-- Reinhard Zumkeller, Jan 12 2013

Maple

a:= n-> Bits[Join](ListTools[Reverse](Bits[Split](n, bits=8))):
seq(a(n), n=0..255);  # Alois P. Heinz, Nov 28 2024

Mathematica

a[n_] := FromDigits[PadLeft[IntegerDigits[n, 2], 8] // Reverse, 2]; Table[a[n], {n, 0, 255}] (* Jean-François Alcover, Dec 26 2015 *)
IntegerReverse[Range[0, 255], 2, 8] (* Paolo Xausa, Nov 28 2024 *)

PARI

A160638(n)=binary(n+256)*vector(9,n,2^n)~\4  \\ M. F. Hasler, Oct 07 2012

PARI

A160638(n)=sum(i=0,7,bittest(n,7-i)<M. F. Hasler, Oct 07 2012

Python

def a(n): return int(bin(n)[2:].zfill(8)[::-1], 2)
print([a(n) for n in range(256)]) # Michael S. Branicky, Jul 13 2022

Formula

a(n) = floor(A030101(n+256)/2). - Reinhard Zumkeller, Jan 12 2013