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

0,2

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

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.

Formula

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

Example

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

Mathematica

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

Prog

(C) int a = 0; for(int i=0; i<8; i++) if(n & (1<<i)) a |= 1<<(7 - i);
(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)<<i)  \\ M. F. Hasler, Oct 07 2012
(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
(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

Crossrefs

Cf. A217589.

Sequence in context: A121374 A336774 A252487 * A188829 A336776 A172532

Adjacent sequences: A160635 A160636 A160637 * A160639 A160640 A160641

Keyword

base,easy,fini,full,nonn,nice

Author

Russ Cox, May 21 2009

Status

approved