A293668 -id:A293668 - cp's OEIS frontend

A255308 Number of times log_2 can be applied to n until the result is not a power of 2. Here log_2 means the base-2 logarithm.

0, 1, 2, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 0

Paul Boddington, Feb 20 2015

Multiplicative because only powers of two have a nonzero value. - Andrew Howroyd, Jul 27 2018

Antti Karttunen, Table of n, a(n) for n = 0..65537

Cf. A209229, A255309.

One less than A293668.

a(n) = if(n < 1, 0, my(e=valuation(n, 2)); if(n == 2^e, 1 + a(e), 0)) \\ Andrew Howroyd, Jul 27 2018

a(n) = 1 + a(log_2(n)) if n is a power of 2, 0 otherwise.

Extended up to a(128) by Antti Karttunen, Sep 30 2018

A292046 The list of distinct values of A072464.

Original entry on oeis.org

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

cp's OEIS Frontend

A255308 Number of times log_2 can be applied to n until the result is not a power of 2. Here log_2 means the base-2 logarithm.

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