# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a181942 Showing 1-1 of 1 %I A181942 #8 Apr 04 2012 10:02:33 %S A181942 -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 A181942 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 A181942 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 A181942 Floor(n/((log n) log log n)) %C A181942 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 A181942 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 A181942 (PARI) A181942(n)=n\(log(n)*log(log(n))) %K A181942 sign %O A181942 2,1 %A A181942 _M. F. Hasler_, Apr 03 2012 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE