# [seqfan] Re: periodicity of expansion of 3/2 in phi-phase A173857

Joerg Arndt arndt at jjj.de
Thu Mar 4 15:55:07 CET 2010

```* Richard Mathar <mathar at strw.leidenuniv.nl> [Mar 04. 2010 15:38]:
>
> The coefficients of expanding 3/2 in the base A001622 look
> strikingly similar to A079978 (=periodic).
> Does this pattern continue for all further digits?

Looks like it:

? default(realprecision,55)
55
? ph=1/((sqrt(5)+1)/2)  \\ NOTE 1/Golden
0.6180339887498948482045868343656381177203091798057628621
? (ph+ph^3/(1-ph^3))/ph
1.500000000000000000000000000000000000000000000000000000

>
> http://research.att.com/~njas/sequences/?q=id:A173857|id:A079978
> 1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,
>
> 1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,
>

In seq A173857 (Expansion of 3/2 in base phi)
should have some an entry
3/2 == 1+ph^2*(1+ph^3+ph^6+ph^9+ph^12+...)
and the offset should be zero (1==ph^0)

> [...]

cheers,   jj

```