|
%I #13 Jan 16 2017 13:53:28
%S 0,1,4,5,24,25,26,27,112,113,114,115,116,117,118,119,480,481,482,483,
%T 484,485,486,487,488,489,490,491,492,493,494,495,1984,1985,1986,1987,
%U 1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001
%N Representation of n in D. E. Knuth's second prefix-unambiguous, order-preserving binary string system.
%C The first two terms are the strings "00" and "01"; all others are binary strings beginning with "1".
%C 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).
%D Donald E. Knuth, "Supernatural Numbers", in D. A. Klarner, editor, The Mathematical Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 310-325.
%D Donald E. Knuth, Selected Papers on Fun and Games. Stanford, California: Center for the Study of Language and Information (2011).
%H Indranil Ghosh, <a href="/A171885/b171885.txt">Table of n, a(n) for n = 0..10000</a>
%H Robert Munafo, <a href="http://mrob.com/pub/math/altnum.html#lexi">Alternative Number Formats</a>, section on "Lexicographic Strings"
%e 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.
%Y Knuth's first system gives A000918 (less its initial term).
%Y Knuth's third system is A010097, the Levenshtein codes.
%K nonn
%O 0,3
%A _Robert Munafo_, Mar 19 2010
|
