Lehmer sequence
In mathematics, a Lehmer sequence is a generalization of a Lucas sequence.[1]
Algebraic relations
If a and b are complex numbers with
under the following conditions:
- Q and R are relatively prime nonzero integers
- is not a root of unity.
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
Lehmer numbers form a linear recurrence relation with
with initial values . Similarly the companions sequence satisfies
with initial values
Reference
- Weisstein, Eric W. "Lehmer Number". mathworld.wolfram.com. Retrieved 2020-08-11.
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