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Lucas Digits Look (Posted on 2016-11-07) Difficulty: 3 of 5
L(N) denotes the Nth Lucas Number.

Find the first three digits of L(2016)

No Solution Yet Submitted by K Sengupta    
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Indirect computation | Comment 2 of 10 |
http://mathworld.wolfram.com/LucasNumber.html
gives a nifty formula
L_n=[phi^n] 

for n>=2 where phi is the golden ratio and [x] denotes the nearest integer function.

Raising the golden ratio to the 2106 power is too large for my calculator, but its common logarithm isn't.

2016log(phi)=421.3190827

Raising 10 to this power allows us to write in scientific notation:

2.084888069x10^421

So the answer is 208


Edited on November 7, 2016, 9:28 am
  Posted by Jer on 2016-11-07 09:25:13

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