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A072398
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Numerator of best approximation to Pi with denominator <= 10^n.
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8
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3, 22, 22, 355, 355, 312689, 1146408, 5419351, 245850922, 2549491779, 21053343141, 21053343141, 1783366216531, 8958937768937, 139755218526789, 428224593349304, 30246273033735921, 66627445592888887
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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LINKS
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EXAMPLE
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A072398(5) = 312689 because A072398(5)/A072399(5) = 312689/99532 is the best rational approximation to Pi with positive denominator <= 10^5 = 100000. This approximation is accurate to 0.00000000092766%.
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MATHEMATICA
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nmax = 17; cv = Convergents[Pi, 2*nmax] // Reverse; a[n_] := Select[cv, Denominator[#] <= 10^n &, 1] // Numerator // First; Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Jan 04 2013 *)
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PROG
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(PARI) for(n=0, 40, print1(numerator(bestappr(Pi, 10^n)), ", ")) \\ Finds these approximations very quickly.
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CROSSREFS
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KEYWORD
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easy,frac,nice,nonn
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AUTHOR
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STATUS
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approved
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