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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 A293343 Adjacent sequences:  A089994 A089995 A089996 * A089998 A089999 A090000 KEYWORD nonn AUTHOR Roger L. Bagula, Jan 14 2004 STATUS approved

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Last modified May 19 02:29 EDT 2019. Contains 323377 sequences. (Running on oeis4.)