mersenneforum.org > Math Lucas–Lehmer sequences and Heronian triangles with consecutive side lengths
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 2016-11-05, 14:18 #1 a nicol   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 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? Attached Thumbnails
 2016-11-08, 05:32 #2 OlderOwl   Nov 2016 18 Posts 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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