A129972 a(n) = 2*floor(log_2(n)) + 1.

1, 3, 3, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13

Offset: 1

Author

Benoit Cloitre, Jun 13 2007

Keywords

• nonn
• easy

Comments

The number of bits needed to write n using Elias gamma coding. - Charles R Greathouse IV, Mar 21 2012

Consists of the n-th odd number (A005408(n) = 2n+1) repeated 2^(n-1) times (since a(n) = a(n-1) except when a(n) > a(n-1) which happens for n a power of 2). - Jonathan Vos Post, Jun 17 2007

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005408.

Cf. A281149 (See the comment section by Charles R Greathouse IV, of this sequence (A129972) ). - Indranil Ghosh, Jan 17 2017

Programs

PARI

a(n)=2*floor(log(n)/log(2))+1

PARI

a(n)=log(n+.5)\log(2)*2+1 \\ Charles R Greathouse IV, Mar 21 2012

PARI

a(n)=2*logint(n,2)+1 \\ Charles R Greathouse IV, Sep 04 2015

Formula

a(n) = Sum_{k=1..n} (-1)^(k-1)*floor(n/k)*mu(k).