What is n-th term of this sequence? 0,1,0,0,1,0,0,0,1,....

[agniabhishek]

0,1,0,0,1,0,0,0,1.....

What is the nth term for this one?
Please help!


- Abhishek Agnihotri

 

[stapel]

0,1,0,0,1,0,0,0,1.....

What is the nth term for this one?

What have you tried? How far have you gotten? You've Googled the sequence and run it through The On-Line Encyclopedia of Integer Sequences, and... then what?

Please be complete. Thank you!

Eliz.

 

[Deleted member 4993]

Start with listing the positions where you have 1's.

01 001 0001 00001 000001 0000001 00000001

.2....5.....9......14.......20.......27.........35 ----- what is Kth number of this sequence?

 

[agniabhishek]

This goes for an infinite series, I presume.
Again, for the convenience, I write the series :
0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1......~

I hope you know what I mean!
Please enlighten me on this for being a noob.


- Abhishek Agnihotri

 

[pka]

Here is the exact mathematical formulation for the nth term.
\(\displaystyle a_n = \left\{ {\begin{array}{ll} {1,} & {\left\lceil {\frac{{ - 3 + \sqrt {9 + 8n} }}{2}} \right\rceil = \frac{{ - 3 + \sqrt {9 + 8n} }}{2}} \\ {0,} & \mbox{else} \\ \end{array} } \right.\)
This assumes that you understand the ceiling function.