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

1,2

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

Prog

(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")

Crossrefs

Cf. A072464, A281149, A281150.

Sequence in context: A115454 A122466 A066511 * A285776 A226032 A373066

Adjacent sequences: A281190 A281191 A281192 * A281194 A281195 A281196

Keyword

nonn,base,changed

Author

Indranil Ghosh, Jan 17 2017

Status

approved