Distinct Substrings In Binary n

[Richard Mathar]

--- Ralf Stephan <ralf at ark.in-berlin.de> wrote:

> You wrote 
> > a(n) = number of distinct (nonempty)
> substrings
> > in the binary representation of n. (Leading
> > zeroes are stripped.)
> > 
> > Offset = 1.
> > 
> > 1,3,2,5,5,5,3,7,8,7,...
> > 
> > For example:
> > The distinct substrings in binary
> representation
> > (1010) of decimal 10:
> > 0,1,10,01,101,010,1010.
> > So a(1) = 7.
> 
> From the definition, this would be A078822 but
> the numbers differ because you don't agree with
> your own definition "Leading zeroes are
> stripped"
> Take away 01 and 010 (as they are 1 and 10,
> resp.)
> and you get A078822(10) = 5
> 
> 
> ralf
> 


I was unclear. By "leading zeros stripped", I
meant that the leading zeroes of binary *n* were
not considered.
(Otherwise we would have included as substings:
0,00,000,0000,00000,000000,....)
:)

Thanks,
Leroy Quet