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Search: id:A153719
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| A153719 |
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Minimal exponents m such that the fractional part of (pi-2)^m obtains a maximum (when starting with m=1). |
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+0
8
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| 1, 2, 3, 4, 5, 39, 56, 85, 557, 911, 2919, 2921, 4491, 11543, 15724, 98040, 110932, 126659
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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 greater 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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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(6)=39, since fract((pi-2)^39)= 0.9586616565..., but fract((pi-2)^k)<=0.9389018... for 1<=k<=38;
thus fract((pi-2)^39)>fract((pi-2)^k) for 1<=k<39 and 39 is the minimal exponent > 5 with this property.
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CROSSREFS
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Cf. A153663, A153671, A153679, A153687, A153695, A153707, A153715, A153723, A154130.
Sequence in context: A060067 A043310 A044907 this_sequence A024637 A037328 A028427
Adjacent sequences: A153716 A153717 A153718 this_sequence A153720 A153721 A153722
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KEYWORD
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nonn,more
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AUTHOR
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Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jan 06 2009
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