A072464 -id:A072464 - cp's OEIS frontend

A292046 The list of distinct values of A072464.

1, 3, 6, 7, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79

Offset: 1

Khalil Fazal, Sep 11 2017

Distinct lengths taken by the Elias omega coding.

Andrey Zabolotskiy, Table of n, a(n) for n = 1..10000
P. Elias, Universal codeword sets and representations of the integers, IEEE Trans. Information Theory 21(2), Mar 1975, pages 194-203.
Wikipedia, Elias omega coding

The list of distinct values of A072464. First differences are A293668.

from math import log
a = [1]
for i in range(1, 66): a.append(i+a[int(log(i, 2))]+1)
print(a)
# Andrey Zabolotskiy, Sep 18 2017

a(26)-a(66) from Andrey Zabolotskiy, Sep 18 2017

A281193 Elias's omega code for n.

Original entry on oeis.org

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

Indranil Ghosh, Jan 17 2017

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).

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

Cf. A072464, A281149, A281150.

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")

cp's OEIS Frontend

A292046 The list of distinct values of A072464.

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