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A181942
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Floor(n/((log n) log log n))
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3
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-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
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OFFSET
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2,1
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COMMENTS
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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.
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LINKS
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PROG
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(PARI) A181942(n)=n\(log(n)*log(log(n)))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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