20161105, 14:18  #1 
Nov 2016
29 Posts 
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 LucasLehmer 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? 
20161108, 05:32  #2 
Nov 2016
1_{8} Posts 
I notice the n+1 series follows the recursive formula S(n) = 4*S(n1)  S(n2) with S(0) = 2 and S(1) = 4 the LucasLemer series LL(I) = S(2^(I))

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