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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)
 OFFSET 1,2 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). 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. 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. EXAMPLE For n = 9, first part is "1110" and the second part is "001". So, a(9) = 1110001. PROG (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)

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Last modified January 24 06:41 EST 2022. Contains 350534 sequences. (Running on oeis4.)