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A089997 a(n) = Floor[Exp[(Composite[n]-Sqrt[Composite[n]*CompositePi[n]])/(-CompositePi[n]+ Sqrt[Composite[n]*CompositePi[n]])]] 0
7, 11, 16, 8, 9, 7, 8, 6, 5, 5, 6, 5, 5, 5, 5, 5, 5, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Complementary function to the log type function of the primes and their distributions as the function of the composites and their distribution.
The result even as an exponential function seems to tend to an asymototic limit.
LINKS
MATHEMATICA
(* manufacture the composite numbers as a function*) p[n_]=n!/Product[Prime[i], {i, 2, PrimePi[n]}] digits=200 a0=Table[p[n]/p[n-1], {n, 2, digits}] c=Delete[Delete[Union[a0], 1], 1] d=Dimensions[c][[1]] Composite[n_]=c[[n]] (* make the log equivalent function*) g[n_]=(Composite[n]-Sqrt[Composite[n]*CompositePi[n]])/(-CompositePi[n]+ Sqrt[Composite[n]*CompositePi[n]]) e=Table[Floor[Exp[g[n]]], {n, 1, d-1}]
CROSSREFS
Sequence in context: A037136 A023486 A284485 * A129188 A022950 A364442
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Jan 14 2004
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)