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A010097 Prefix (or Levenshtein) codes for natural numbers. 2


%S 0,2,12,13,112,113,114,115,232,233,234,235,236,237,238,239,3840,3841,

%T 3842,3843,3844,3845,3846,3847,3848,3849,3850,3851,3852,3853,3854,

%U 3855,7712,7713,7714,7715

%N Prefix (or Levenshtein) codes for natural numbers.

%D R. E. Krichevsky, Szhatie i poisk informatsii (Compressing and searching for information), Moscow, 1988, ISBN 5-256-00325-9.

%D D. E. Knuth, "Supernatural Numbers", in D. A. Klarner, editor, The Mathematical Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 310-325. [_Robert Munafo_, Mar 19 2010]

%D D. E. Knuth, Selected Papers on Fun and Games, to be published (later in 2010). [_Robert Munafo_, Mar 19 2010]

%H Matthew House, <a href="/A010097/b010097.txt">Table of n, a(n) for n = 0..10000</a>

%H R. Munafo, <a href="http://mrob.com/pub/math/altnum.html#lexi">Alternative Number Formats</a>, section on "Lexicographic Strings". [_Robert Munafo_, Mar 19 2010]

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Levenshtein_coding">Levenshtein coding</a>

%F The code for n is found as follows: from right to left, the truncated (without the leading 1) binary representations of n, floor(log_2(n)), floor(log_2(floor(log_2(n)))), etc., are written as long as they consist of at least one bit; then we write a 0 followed by log*(n) 1's.

%Y Knuth articles also give A000918 and A171885. [_Robert Munafo_, Mar 19 2010]

%K nonn

%O 0,2

%A _Leonid Broukhis_

%E Offset corrected by _Matthew House_, Aug 15 2016

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Last modified April 20 08:54 EDT 2021. Contains 343125 sequences. (Running on oeis4.)