

A171885


Representation of n in D. E. Knuth's second prefixunambiguous, orderpreserving binary string system.


7



0, 1, 4, 5, 24, 25, 26, 27, 112, 113, 114, 115, 116, 117, 118, 119, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001
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OFFSET

0,3


COMMENTS

The first two terms are the strings "00" and "01"; all others are binary strings beginning with "1".
With the important exception of a(1) = 1, when expressed in binary, any value not appearing in this sequence appears as an initial substring of later terms. For example, 6 (110) is an initial substring of 27 (11011).


REFERENCES

Donald E. Knuth, "Supernatural Numbers", in D. A. Klarner, editor, The Mathematical Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 310325.
Donald E. Knuth, Selected Papers on Fun and Games. Stanford, California: Center for the Study of Language and Information (2011).


LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..10000
Robert Munafo, Alternative Number Formats, section on "Lexicographic Strings"


EXAMPLE

The representations start: 0 = "00"; 1 = "01"; 2 = "100"; 3 = "101"; 4 = "11000"; 5 = "11001"; 6 = "11010"; 7 = "11011"; 8 = "1110000"; 9 = "1110001"; and so on. See the references for longer lists and fuller explanation.


CROSSREFS

Knuth's first system gives A000918 (less its initial term).
Knuth's third system is A010097, the Levenshtein codes.
Sequence in context: A291670 A176957 A010302 * A063986 A039583 A042123
Adjacent sequences: A171882 A171883 A171884 * A171886 A171887 A171888


KEYWORD

nonn


AUTHOR

Robert Munafo, Mar 19 2010


STATUS

approved



