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A137994
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a(n) is the smallest integer > a(n-1) such that {Pi^a(n)} < {Pi^a(n-1)}, where {x} = x - floor(x), a(1)=1.
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12
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1, 3, 81, 264, 281, 472, 1147, 2081, 3207, 3592, 10479, 12128, 65875, 114791, 118885
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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a(3)=81, since fract((Pi^81)=0.0037011283.., but fract(Pi^k)>=0.0062766802... for 1<=k<=80; thus fract(Pi^81)<fract(Pi^k) for 1<=k<81. [Hieronymus Fischer, Jan 06 2009]
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MATHEMATICA
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$MaxExtraPrecision = 10000;
p = .999;
Select[Range[1, 5000],
If[FractionalPart[Pi^#] < p, p = FractionalPart[Pi^#]; True] &] (* Robert Price, Mar 12 2019 *)
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PROG
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(PARI) default(realprecision, 10^4); print1(a=1); for(i=1, 100, f=frac(Pi^a); until( frac(Pi^a++)<f, ); print1(", "a))
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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