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 A160638 Bit-reversed 8-bit binary numbers. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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< 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

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Last modified April 15 20:47 EDT 2024. Contains 371696 sequences. (Running on oeis4.)