A181942 Floor(n/((log n) log log n))

-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, 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, 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

Offset

2,1

Comments

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.)

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.

Links

Table of n, a(n) for n=2..99.

Prog

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

Crossrefs

Sequence in context: A193288 A050548 A261845 * A140447 A038934 A262285

Adjacent sequences: A181939 A181940 A181941 * A181943 A181944 A181945

Keyword

sign

Author

M. F. Hasler, Apr 03 2012

Status

approved