A255308 -id:A255308 - cp's OEIS frontend

A072464 Code word lengths for non-redundant MML code for positive integers.

1, 3, 3, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13

Offset: 1

Michael Somos, Jun 19 2002

Also the number of bits needed to write the universal code for an Elias omega coding. This seems to differ (by 1 bit) from the Elias omega coding used in A147814 and A147764. - Charles R Greathouse IV, Mar 26 2012

			Code words: 1, 010, 011, 000100, 000101, 000110, 000111, ...

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Lloyd Allison, Integer Distribution.
Wikipedia, Elias omega coding

Cf. A147814, A147764, A255308 (first differences), A292046 (list of distinct values).

a(n) = local(l); if( n<2, n>0, l = length( binary(n)); l + a(l-1))

A255309 Number of times log_2 can be applied to n until the result is either 1 or not a power of 2. Here log_2 means the base-2 logarithm.

Original entry on oeis.org

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

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

Cf. A000079 (2^n), A007814 (2-adic valuation of n), A209229, A255308.

nbi(n) = {my(nb = 0); if ((ispower(n, ,&m) && (m==2)) || (n==2), return(nbi(valuation(n, 2))+1);); nb;}
a(n) = { my(nb = 0); if ((ispower(n, ,&m) && (m==2)) || (n==2), return(nbi(valuation(n, 2))+1);); nb;} \\ Michel Marcus, Mar 11 2015; corrected Jun 13 2022

A255309(n) = { my(k=0); while((n>1)&&!bitand(n,n-1),n = valuation(n,2); k++); (k); }; \\ Antti Karttunen, Sep 30 2018

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

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

A293668 First differences of A292046.

Original entry on oeis.org

1, 2, 3, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Andrey Zabolotskiy, Oct 14 2017

a(n) is also the length of n-th run of consecutive integers in the complement of A292046, starting from the 1st run "4, 5".

This sequence is invariant under the following transform: subtract 1 from every term, eliminate zeros. Other sequences with this property include A001511 and other generalized ruler functions, A002260, A272729.

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

Cf. A001511, A002260, A230864, A255308, A272729, A292046.

A293668(n) = { my(k=1); while(n && !bitand(n,n-1),n = valuation(n,2); k++); (k); }; \\ Antti Karttunen, Sep 30 2018

a(0) = 1, a(n) = A292046(n+1)-A292046(n) for n>0.
If n = 2^k, a(n) = a(k)+1; otherwise a(n) = 1.
a(n) = A255308(n) + 1.
a(n) = O(log*(n)), where log* is the iterated logarithm. More precisely, a(n) <= A230864(n+1)+1.

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A072464 Code word lengths for non-redundant MML code for positive integers.

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A255309 Number of times log_2 can be applied to n until the result is either 1 or not a power of 2. Here log_2 means the base-2 logarithm.

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A293668 First differences of A292046.

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