Series of EllipticK[x]/Pi

[Jeffrey Shallit]

>  {2,3,2,4,2,3,2,5,2,3,2,4,2,3,2,6,2,3,2,4,2,3,2,5,2,3,2,4,2,3,2,7,2,3,2,4,
>   2,3,2,5,2,3,2,4,2,3,2,6,2,3,2,4,2,3,2,5,2,3,2,4,2,3,2,8,2,3,2,4,2,3,2,5,
>   2,3,2,4,2,3,2,6,2,3,2,4,2,3,2,5,2,3,2,4,2,3,2,7
> 
> a nicely regular thing, that can be recursively symbolised in Mathematica as:
> 
> In[91]:=
> 2+Flatten[Fold[{#1,#2,#1}&,0,Range[6]]]
> Out[91]=
>  {2,3,2,4,2,3,2,5,2,3,2,4,2,3,2,6,2,3,2,4,2,3,2,5,2,3,2,4,2,3,2,7,2,3,2,4,
>   2,3,2,5,2,3,2,4,2,3,2,6,2,3,2,4,2,3,2,5,2,3,2,4,2,3,2,8,2,3,2,4,2,3,2,5,
>   2,3,2,4,2,3,2,6,2,3,2,4,2,3,2,5,2,3,2,4,2,3,2,7,
>   2,3,2,4,2,3,2,5,2,3,2,4,2,3,2,6,2,3,2,4,2,3,2,5,2,3,2,4,2,3,2}

This sequence appears to be just 2 + nu_2 (n), where nu_2 is the
exponent of the highest power of 2 dividing n.

Jeffrey Shallit, Computer Science, University of Waterloo,
Waterloo, Ontario  N2L 3G1 Canada shallit at graceland.uwaterloo.ca
URL = http://math.uwaterloo.ca/~shallit/