login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A168160 Number of 0's in the matrix whose lines are the binary expansion of the numbers 1,...,n. 1

%I #3 Jul 14 2012 11:32:32

%S 0,2,2,7,8,9,9,19,21,23,24,26,27,28,28,47,50,53,55,58,60,62,63,66,68,

%T 70,71,73,74,75,75,111,115,119,122,126,129,132,134,138,141,144,146,

%U 149,151,153,154,158,161,164,166,169,171,173,174,177,179,181,182,184,185,186

%N Number of 0's in the matrix whose lines are the binary expansion of the numbers 1,...,n.

%C The matrix is to be taken of minimal size, i.e., have n lines and the number of columns needed to write n in base 2 in the last line, A070939(n). Otherwise said, there is no zero column.

%C The number of zeros in the last line of the matrix is given by A023416(n).

%C One has a(n)=a(n-1) iff n = 2^k-1 for some k.

%F A168160(n)=n*A070939(n)-A000788(n).

%e a(4)=7 is the number of zeros in the matrix

%e [001] /* = 1 in binary */

%e [010] /* = 2 in binary */

%e [011] /* = 3 in binary */

%e [100] /* = 4 in binary */

%o (PARI) A168160(n)=n*#binary(n)-sum(i=1,n,norml2(binary(i)))

%Y Cf. A059015.

%K base,nonn

%O 1,2

%A _M. F. Hasler_, Nov 22 2009

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)