[seqfan] Re: Fibonaroot

[Eric Angelini]

Many thanks, Hans!
I've appreciated the search for S[j,k] seq. and the loop {9}, from 'smallest' [9,9]!
Best,
Sorry again for the error in S(3)...
É.
Propulsé d'un aPhone



Le 14 juil. 2013 à 00:40, "Hans Havermann" <gladhobo at teksavvy.com> a écrit :

> Eric Angelini:
> 
>> If we call S(k) a sequence with the seed [1,k],... is there a S(k) sequence which doesn't (end in a loop)?
> 
> 
> For k<10^7, everything evolves into one of three loops:
> 
> {1,1,2,3,5,8,13,21,34,1,8,9,17,8,25,6,31,37,68,6,74,8,1,9}, from smallest k = 1.
> 
> {1,7,8,6,14,20,34,9,43,52,95,147,8,155,163,318,4,322,326,9,335,344,4,6}, from smallest k = 3. [Your S(3) contained an error.]
> 
> {1,6,7,13,20,6,8,14,4,9,13,4,17,21,38,59,97,156,1,157,158,9,167,176}, from smallest k = 4.
> 
> Allowing seeds [j,k], j>1, the latter two loops may be generated from 'smallest' [2,1] and [3,1], respectively. I found two additional loops:
> 
> {6,6,12,9,21,30,6,9}, from 'smallest' [3,3].
> 
> {9}, from 'smallest' [9,9].
> 
> 
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