Longest Lucas seq. from start to "n"

[Eric Angelini]

Yes, sorry Max -- no Lucas numbers, no negative terms.

15 1 16 17
13 2 15 17
11 3 14 17
 9 4 13 17
 7 5 12 17
 4 1  5  6 11 17 <-- "Llatest entry of integer n=17 in a Lucas seq"
 4 3  7 10 17
 7 1  8  9 17

Best,
É.

 

-----Message d'origine-----
De : Max Alekseyev [mailto:maxale at gmail.com] 
Envoyé : jeudi 18 octobre 2007 12:39
À : Eric Angelini
Cc : seqfan at ext.jussieu.fr
Objet : Re: Longest Lucas seq. from start to "n"

Eric,

Your problem formulation is unclear.

Do you wand a sequence of Lucas numbers or (generic) Lucas sequence?
These are different beasts:
http://mathworld.wolfram.com/LucasNumber.html
http://mathworld.wolfram.com/LucasSequence.html

Do you want all elements of your sequence be positive (or
non-negative) integers?

Max

On 10/18/07, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
> Hello SeqFans,
> I guess this is (very) old hat -- sorry.
>
> I want to insert "17" (for instance) as later as
> possible in a Lucas seq. I found by hand that the
> seq 4 1 5 6 11 [17] 28...  is the answer (5 terms
> before "17"; the seq 7 1 8 9 [17] 26... has 4)
>
> What is the general method to find those? There
> must be a seq in the OEIS linking n to the length
> of its "latest entry" in a Lucas sequence -- but
> I cannot find it.
>
> What would be the longest such chain including 2007?
>
> Best,
> É.
>
>