deletions | additions       diff --git a/section_Input_Output_Sequences_begin__.tex b/section_Input_Output_Sequences_begin__.tex  index d60279e..f9adac0 100644  --- a/section_Input_Output_Sequences_begin__.tex  +++ b/section_Input_Output_Sequences_begin__.tex 
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1,3,1,3,1,3,1,3... & A047891\\  1,4,1,4,1,4,1,4... & A082298\\  1,1,2,1,2,1,2,1... & A001003\\  1,2,2,2,2,2,2,2... & A151374\\  1,5,2/5,13/5,10/13,29/13,26/29,61/29,58/61,125/61... & A134425\\  \end{matrix}  \end{equation}  There is potentially a very powerful concept available here, where we will be able to write a functional form of sorts for expressions such as $n \;\mod\;m$.  It is becoming increasingly clear that there may be two sequences involved in describing certain hard to fit members. Then the input series is actually of the form \begin{equation}  C_0,a_1,b_1,a_2,b_2,a_3,b_3...  \end{equation}  where $C_0$ is just a leading coefficient, and then the two sequences $a$ and $b$ progress with their description. Then many sequences will start with $C_0=1$, if they start with $1$.  Then sequence $A134425$ actually has two input sequences \begin{equation}  a=5,13/5,29/13,61/29,125/61...\\  b=2/5,10/13,26/29,58/61...\\  \end{equation}  We then see that for the sequence \begin{equation}  t=1,5,13,29,61,125...\\  \end{equation}  we can define \begin{equation}  a_i = \frac{t_{i+1}}{t_{i}}  \end{equation}  it then follows that \begin{equation}  b_{i}=\frac{2}{a_i}  \end{equation}