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A153717
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Minimal exponents m such that the fractional part of (Pi-2)^m obtains a minimum (when starting with m=1).
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8
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1, 20, 23, 24, 523, 2811, 3465, 3776, 4567, 6145, 8507, 9353, 19790, 41136, 62097, 72506, 107346
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OFFSET
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1,2
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COMMENTS
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Recursive definition: a(1)=1, a(n) = least number m>a(n-1) such that the fractional part of (Pi-2)^m is less than the fractional part of (Pi-2)^k for all k, 1<=k<m.
The next such number must be greater than 200000.
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LINKS
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FORMULA
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Recursion: a(1):=1, a(k):=min{ m>1 | fract((Pi-2)^m) < fract((Pi-2)^a(k-1))}, where fract(x) = x-floor(x).
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EXAMPLE
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a(3)=23, since fract(((Pi-2)^23)=0.0260069.., but fract((Pi-2)^k)>=0.1326... for 1<=k<=22; thus fract((Pi-2)^23)<fract((Pi-2)^k) for 1<=k<23.
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MATHEMATICA
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$MaxExtraPrecision = 100000;
p = 1; Select[Range[1, 10000],
If[FractionalPart[(Pi - 2)^#] < p, p = FractionalPart[(Pi - 2)^#];
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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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STATUS
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approved
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