valuation(2, prime(n)-1)

[benoit]

Letting S(n)=sum(i=2, n, valuation(2, prime(i)-1) )

I suppose limit n-->infty S(n)/n = 2

I asked myself if (2n-S(n))/sqrt(n) is bounded with S(n)<2n and if 
limit n-->infty (2n-S(n))/sqrt(n) exist ?

With n=40000 I obtained (2n-S(n))/sqrt(n) = 0.7....

sum(i=2,40000,valuation(prime(i)-1,2))=79859 and 
(2*40000-79859)/sqrt(40000)=0.705

I don't believe that's specific to primes but thanks for confirming or 
not this fact.

B Cloitre