

A010097


Prefix (or Levenshtein) codes for natural numbers.


2



0, 2, 12, 13, 112, 113, 114, 115, 232, 233, 234, 235, 236, 237, 238, 239, 3840, 3841, 3842, 3843, 3844, 3845, 3846, 3847, 3848, 3849, 3850, 3851, 3852, 3853, 3854, 3855, 7712, 7713, 7714, 7715
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OFFSET

0,2


REFERENCES

R. E. Krichevsky, Szhatie i poisk informatsii (Compressing and searching for information), Moscow, 1988, ISBN 5256003259.
D. E. Knuth, ``Supernatural Numbers'', in D. A. Klarner, editor, The Mathematical Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 310325. [Robert Munafo, Mar 19 2010]
D. E. Knuth, Selected Papers on Fun and Games, to be published (later in 2010). [Robert Munafo, Mar 19 2010]


LINKS

Matthew House, Table of n, a(n) for n = 0..10000
R. Munafo, Alternative Number Formats, section on "Lexicographic Strings". [Robert Munafo, Mar 19 2010]
Wikipedia, Levenshtein coding


FORMULA

The code for n is found as follows: from right to left, the truncated (without the leading 1) binary representations of n, int(log2(n)), int(log2(int(log2(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.


CROSSREFS

Knuth articles also give A000918 and A171885. [Robert Munafo, Mar 19 2010]
Sequence in context: A072483 A081539 A141273 * A103761 A286241 A078755
Adjacent sequences: A010094 A010095 A010096 * A010098 A010099 A010100


KEYWORD

nonn


AUTHOR

Leonid Broukhis


EXTENSIONS

Offset corrected by Matthew House, Aug 15 2016


STATUS

approved



