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In mathematics, a Lehmer sequence is a generalization of a Lucas sequence.[1]
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 companion sequence satisfies
with initial values
References[edit]
- ^ Weisstein, Eric W. "Lehmer Number". mathworld.wolfram.com. Retrieved 2020-08-11.