123 is a Lucas number. It is the eleventh member of the Mian-Chowla sequence.
Using Ln−2 = Ln − Ln−1, one can extend the Lucas numbers to negative integers to obtain a doubly infinite sequence:
..., −11, 7, −4, 3, −1, 2, 1, 3, 4, 7, 11, ... (terms L n {\displaystyle L_{n}} for − 5 ≤ n ≤ 5 {\displaystyle -5\leq {}n\leq 5} are shown).
The formula for terms with negative indices in this sequence is
L − n = ( − 1 ) n L n . {\displaystyle L_{-n}=(-1)^{n}L_{n}.\!}