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Search: id:A154132
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| A154132 |
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Minimal exponents m such that the fractional part of (4/3)^m increases monotonically (when starting with m=1). |
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+0
2
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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 (4/3)^m is greater than the
fractional part of (4/3)^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((4/3)^m) > fract((4/3)^a(k-1))}, where fract(x) = x-floor(x).
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EXAMPLE
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a(4)=39, since fract((4/3)^39)= 0.999186..., but fract((4/3)^k)<0.9887... for 1<=k<=38;
thus fract((4/3)^39)>fract((4/3)^k) for 1<=k<39 and 39 is the minimal exponent > 8 with this property.
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CROSSREFS
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Cf. A153663, A153671, A153703, A153710, A154140, A154148.
Cf. A002379, A064628.
Sequence in context: A020047 A068107 A091073 this_sequence A152458 A087971 A127919
Adjacent sequences: A154129 A154130 A154131 this_sequence A154133 A154134 A154135
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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 11 2009
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