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Old 2013-05-29, 19:59   #1
Mar 2013

28 Posts
Default Conjecture about Mersenne primes and non-primes v2

I posted a tread about the solution of the riddle "the 4 button room".
My conjecture was that A056295(n) is related to 2^n-1 being a prime or not.
(search on this site).

I wanted to compare A056295(n) to a smooth version of that series.
At the time I hade no test quantity but I thought of - a very primitive - one now,
which is simply the mean of the number for n-1 and n+1, i.e. $TQ=(A056295(n-1)+ A056295(n+1))/2$ with which I compare A056295(n)

I find that there is a perfect correlation between A056295(n)/TQ and the number of factors of 2^n-1 up to n=10. That is good beginning. I can't show you the graph but it is simple enough to establish.
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