Blocks within the period of Lucas sequence

Abstract

In this paper, we consider the periodic nature of the sequence of Lucas numbers L_n defined by the recurrence relation L_n= L_(n-1)+L_(n-2); for all n≥2; with initial condition L_0=2 and L_1=1. For any modulo m>1, we introduce the ‘blocks’ within this sequence by observing the distribution of residues within a single period of Lucas sequence. We show that length of any one period of the Lucas sequence contains either 1,2 or 4 blocks.

Keywords

• fibonacci sequence, lucas sequence, periodicity of lucas sequence