The Lucas Numbers

Number Theory Level 2

If the Lucas numbers be defined by the recurrence relation L 0 = 2 L_0 = 2 L 1 = 1 L_1 = 1 L n = L n − 1 + L n − 2 L_{n} = L_{n-1} + L_{n-2} . Then find the value of L 10 L_{10} .


The answer is 123.

Eddie The Head by Eddie The Head , 27, India

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2 solutions

Debashis Mallik
May 23, 2014

The sequence is: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123 ... like that. As L1 = 1, L10 should be 123.

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Python Code: 

>>> def Lucas(n):
...         if not n: return 2
...         if n==1: return 1
...         return Lucas(n-1) + Lucas(n-2)
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