The sequence of the first twelve Lucas numbers is: 2,1,3,4,7,11,18,29,47 …
Please write a program for calculating the Lucas number Ln given the number n. Print out the results given:
a) n=2 ; b) n=5 and c) n=10
(**please answer in Python**)
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The sequence of the first twelve Lucas numbers is: 2,1,3,4,7,11,18,29,47 … Please write a program for...
The Lucas Numbers are a sequence very similar to the Fibonacci sequence discussed in class, the only difference being that the Lucas Numbers start with 10-2 L,-1 as opposed to Fibonacci's Fo = 0 and F1 = 1, concretely, they are defined by Lo = 2, L,-1 and Ln-Ln-l + Ln-2 for n > 1 Write a Python function called first D_digit Lucas that takes an integer argument D less than 30 and returns the first D-digit Lucas number. For...
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The Lucas numbers L(n) have almost the same definition as the Fibonacci numbers: If n = 1 if n- 2 L(n 1) L(n - 2) if n > 2. 12, as in Theorem 3.6. Prove that L(n)-α, β n for all n E N. Use strong induction Let α = 1 + v/5 and β-- Proof. First, note that and L(2) suppose as inductive hypothesis that L()-α4 β, for all i k, for some k > 2. Then l(k) =...
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