In mathematics, a Lehmer sequence is a generalization of a Lucas sequence.[1]

Algebraic relations

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If a and b are complex numbers with

 
 

under the following conditions:

Then, the corresponding Lehmer numbers are:

 

for n odd, and

 

for n even.

Their companion numbers are:

 

for n odd and

 

for n even.

Recurrence

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Lehmer numbers form a linear recurrence relation with

 

with initial values  . Similarly the companion sequence satisfies

 

with initial values  

References

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  1. ^ Weisstein, Eric W. "Lehmer Number". mathworld.wolfram.com. Retrieved 2020-08-11.