A014550 Binary reflected Gray code.

0, 1, 11, 10, 110, 111, 101, 100, 1100, 1101, 1111, 1110, 1010, 1011, 1001, 1000, 11000, 11001, 11011, 11010, 11110, 11111, 11101, 11100, 10100, 10101, 10111, 10110, 10010, 10011, 10001, 10000, 110000, 110001, 110011, 110010, 110110

Offset: 0

Author

Eric W. Weisstein

Keywords

• nonn
• nice
• easy

References

• M. Gardner, The Binary Gray Code. Ch. 2 in Knotted Doughnuts and Other Mathematical Entertainments. New York: W. H. Freeman, 1986.
• C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 392.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..8191
• Dominique Désérable, Versatile Topology for Two-Dimensional Cellular Automata, Advances in Cellular Automata, Emergence, Complexity and Computation (ECC Vol 52) Springer, Cham (2025), Ch. 6, pp. 151-186.
• Eric Weisstein's World of Mathematics, Gray Code
• Wikipedia, Gray code

Crossrefs

Same sequence in decimal: A003188.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      (b-> 10^b +a(2^(b+1)-1-n))(ilog2(n)))
    end:
seq(a(n), n=0..50);  # Alois P. Heinz, Nov 01 2008

Mathematica

a[n_] := a[n] = (b = Floor[Log[2, n]]; If[n <= 1, n, 10^b + a[2^(b + 1) - 1 - n]]); Table[a[n], {n, 0, 36}] (* Jean-François Alcover, Oct 11 2012, after Alois P. Heinz *)

PARI

a(n)=fromdigits(binary(bitxor(n, n>>1))) \\ Charles R Greathouse IV, Feb 06 2017

Python

def A014550(n): return int(bin(n^n>>1)[2:]) # Chai Wah Wu, May 31 2024

Extensions

More terms from Larry Reeves (Larryr(AT)acm.org), Sep 05 2000