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A281149 Elias gamma code (EGC) for n. 6
1, 100, 101, 11000, 11001, 11010, 11011, 1110000, 1110001, 1110010, 1110011, 1110100, 1110101, 1110110, 1110111, 111100000, 111100001, 111100010, 111100011, 111100100, 111100101, 111100110, 111100111, 111101000, 111101001, 111101010, 111101011, 111101100, 111101101, 111101110 (list; graph; refs; listen; history; text; internal format)



This sequence is the binary equivalent of A171885 for n>=1 and is also mentioned in the example section of the same.

The number of bits of a(n) is equal to A129972(n).

Unary(n) = A105279(n-1).


Indranil Ghosh, Table of n, a(n) for n = 1..10000

J. Nelson Raja, P. Jaganathan and S. Domnic, A New Variable-Length Integer Code for Integer Representation and Its Application to Text Compression, Indian Journal of Science and Technology, Vol 8(24), September 2015.


For a given integer n, it is stored in two parts. The first part equals 1+floor(log_2 n) and the second part equals n-2^(floor(log_2 n)). The first part is stored in unary and the second part is stored in binary using floor(log_2 n) bits. Now the first and the second parts are concatenated to give the answer.


For n = 9, first part is "1110" and the second part is "001". So, a(9) = 1110001.



def unary(n):

....return "1"*(n-1)+"0"

def elias_gamma(n):

....if n ==1:

........return "1"

....k=int(math.log(n, 2))

....fp=unary(1+k)    #fp is the first part

....sp=n-2**(k)      #sp is the second part

....nb=k             #nb is the number of bits used to store sp in binary


....if len(sp)<nb:


....return fp+sp


Cf. A105279 (unary code for n), A129972, A171885.

Sequence in context: A063010 A215022 A094027 * A204582 A204583 A092633

Adjacent sequences:  A281146 A281147 A281148 * A281150 A281151 A281152




Indranil Ghosh, Jan 16 2017



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Last modified February 18 13:07 EST 2018. Contains 299322 sequences. (Running on oeis4.)