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Search: id:A108186
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| A108186 |
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New approximation of PrimePi based on x/(log[x]-1) and Integrate[x/Log[x],{x,2,n}] starting at n=10. |
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+0
1
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| 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 23, 24
(list; graph; listen)
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OFFSET
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10,1
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COMMENT
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A singularity exists at low n value. Average error in 10 to 250 is 1.51867 error = Table[Floor[Sqrt[(y /. NSolve[( x/(Log[x] - 1) + y)/100 - Sqrt[y*x/( Log[x] - 1)]/10 == 0, y][[1]])*(y /. NSolve[(x/(Log[ x] - 1) + y)/100 - Sqrt[y*x/(Log[x] - 1)]/10 == 0, y][[2]])]] - PrimePi[x], {x, 10, 250}]
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FORMULA
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x1=x/(Log[x]-1) y1=Integrate[x/Log[x], {n, 2, n}] f[n]=Solve[(x1+y1)/100==(x1*y1)^(1/2)/10, y1] a(n) = Sqrt[f[n][[1]]*f[[n][[2]]]
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MATHEMATICA
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PiN = Table[Floor[Sqrt[(y /. NSolve[(x/(Log[x] - 1) + y)/100 - Sqrt[y*x/(Log[x] - 1)]/10 == 0, y][[1]])*(y /. NSolve[(x/(Log[x] - 1) + y)/100 - Sqrt[y*x/(Log[x] - 1)]/10 ==0, y][[2]])]], {x, 10, 250}]
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CROSSREFS
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Sequence in context: A021853 A092616 A096251 this_sequence A024818 A076236 A072520
Adjacent sequences: A108183 A108184 A108185 this_sequence A108187 A108188 A108189
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 14 2005
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