Lehmer number

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In mathematics, a Lehmer number is a generalization of a Lucas sequence.

Algebraic relations[edit]

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[edit]

Lehmer numbers form a linear recurrence relation with

with initial values . Similarly the companions sequence satisfies

with initial values .