A281149 Elias gamma code (EGC) for n.

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

Offset: 1

Author

Indranil Ghosh, Jan 16 2017

Keywords

• nonn
• base

Comments

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).

Examples

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

Links

• 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.

Crossrefs

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

Programs

Python

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
    sp=bin(sp)[2:]
    if len(sp)
				

Formula

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.