A281193 Elias's omega code for n.

0, 100, 110, 101000, 101010, 101100, 101110, 1110000, 1110010, 1110100, 1110110, 1111000, 1111010, 1111100, 1111110, 10100100000, 10100100010, 10100100100, 10100100110, 10100101000, 10100101010, 10100101100, 10100101110, 10100110000, 10100110010, 10100110100

Offset: 1

Author

Indranil Ghosh, Jan 17 2017

Keywords

• nonn
• base

Comments

The idea of the Elias omega code is similar to that of the Elias delta code (A281150), except that the length of the codeword in the omega code is recursively encoded.

The number of bits in a(n) is equal to A072464(n).

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..10000
• Khalid Sayood (Editor), Lossless Compression Handbook, Chapter 3 - Universal Codes, p. 59, section 3.6.
• Wikipedia, Elias omega coding

Crossrefs

Cf. A072464, A281149, A281150.

Programs

Python

def E(n):
    s=""
    if n==1:
        return "0"
    else:
        b=(bin(n)[2:])
        s+=E(len(b)-1)+b
    return s
def elias_omega(n):
    return int(E(n)[1:]+"0")