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Old 2016-11-05, 14:18   #1
a nicol
 
Nov 2016

29 Posts
Default Lucas–Lehmer sequences and Heronian triangles with consecutive side lengths

I noticed this demonstration via Wolfram http://demonstrations.wolfram.com/In...veSideLengths/

Titled: Integral Grid Triangles with Consecutive Side Lengths

If we look at the solutions for 2,4,8,16,32..

We get Heronian triangles where the n +1 sides are of length: 14,194,37634,1416317954,2005956546822746114..

http://i.imgur.com/yHByck5.png

Obviously these are the same values as the classic Lucas-Lehmer sequence with a starting value of 4.

Is there any connection between the primality test for Mersenne numbers and these triangles? Do they help us visualise the proof in any way?
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Old 2016-11-08, 05:32   #2
OlderOwl
 
Nov 2016

18 Posts
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I notice the n+1 series follows the recursive formula S(n) = 4*S(n-1) - S(n-2) with S(0) = 2 and S(1) = 4 the Lucas-Lemer series LL(I) = S(2^(I))
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