Longest Lucas seq. from start to "n"

[Eric Angelini]

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.