[seqfan] Re: %N A093086:some confusion(?)

[Richard Mathar]

http://list.seqfan.eu/pipermail/seqfan/2010-March/004105.html

zs> Date: Fri, 19 Mar 2010 20:44:42 -0700 (PDT)
zs> From: zak seidov <zakseidov at yahoo.com>
zs> Subject: [seqfan]  %N A093086:some confusion(?)
zs> 
zs> isn't here some confusion?
zs> 
zs> According to defn:
zs> %N A093086 "Fibonacci in digits": start with a(1)=1, a(2)=1; repeatedly adjoin digits 
zs>                of sum of previous two terms
zs> 
zs>     first 8 terms are OK: 1,1,2,3,5,8,1,3

The description is not very well drafted, but the sequence itself is
"well designed." At each iteration of adding new digits, one looks
at a pointer to one of the previous digits and adds the two digits
at the pointer and right after it, and appends the digits. Then moves the
pointer by one position, independent of the number of digits the sum had.
So after a while, the pointer is lagging more and more behind:

1,1
^pointer, append 1+1=2
1,1,2
  ^pointer moved by one position, append 1+2=3
1,1,2,3
  ^pointer moved by one position, append 1+2=3
1,1,2,3
    ^pointer moved by one position, append 2+3=5
1,1,2,3,5
      ^pointer moved by one position, append 3+5=8
1,1,2,3,5,8
        ^pointer moved by one position, append 5+8=1,3
1,1,2,3,5,8,1,3
          ^pointer moved by one ( !) position, append 8+1=9
1,1,2,3,5,8,1,3,9
            ^pointer moved by one ( !) position, append 1+3=4

Proposed comment to A093086:

(i) Initialize an index i=1, pointing to a(1). (ii) Calculate a(i)+a(i+1)
(iii) Append the one or two digits of the sum to the current terms. (iv) Increase i to i+1. (v) Loop back at (ii) and iterate.