Longest Lucas seq. from start to "n"

[Max Alekseyev]

On 10/18/07, Peter Pein <petsie at dordos.net> wrote:

> After doing a quick hack in Mathematica and feeding the sequence to OEIS
> I get http://www.research.att.com/~njas/sequences/A088858 as answer.
> This sequence does restrict to positive elements of the Lucas sequence.

A088858 restricts the first term of a Fibonacci-like sequence to the value 1.
In the new  sequence A134299 there is no such restriction, the first
term may be any non-negative number.
Therefore, A088858 provides a lower bound for A134299, i.e.,
A088858(n) <= A134299(n) for all n. Moreover, since we can always
prepend 1,0 to sequences considered in A088858 still keeping them
Fibonacci-like, A088858(n)+2 <= A134299(n) for all n.

It may be interesting to consider sequence of those n that
A088858(n)+2 = A134299(n).

Max