20130529, 19:59  #1 
Mar 2013
2 Posts 
Conjecture about Mersenne primes and nonprimes 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^n1 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 n1 and n+1, i.e. $TQ=(A056295(n1)+ A056295(n+1))/2$ 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^n1 up to n=10. That is good beginning. I can't show you the graph but it is simple enough to establish. 
20130530, 12:32  #2  
Nov 2003
7460_{10} Posts 
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