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Floor(n/((log n) log log n))
3

%I #8 Apr 04 2012 10:02:33

%S -7,29,8,6,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,

%T 7,7,7,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,

%U 10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,14,14

%N Floor(n/((log n) log log n))

%C The function f(x) = x/((log x) log log x) has a minimum of ~ 5.2 at x ~ 9.39 and is increasing for larger x. The growth of this function is related to the growth of prime numbers. As a result, the function f is a relatively fast growing function with the property that the map p -> nextprime(f^-1(p)) = A181943(p) seems to have p -> floor(f(p)) = A181942(p), or p->floor(f(p)/2)*2+1, as left inverse "almost everywhere"(?) on the primes. (The function x/(log x)^2 also has this property, but is not growing as fast.)

%C This is the "decoding function" of A181922: Repeated application to the n-th element of that sequence successively yields the n preceding smaller primes, at least for n<= 1000.

%o (PARI) A181942(n)=n\(log(n)*log(log(n)))

%K sign

%O 2,1

%A _M. F. Hasler_, Apr 03 2012