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Search: id:A153703
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| A153703 |
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Minimal exponents m such that the fractional part of e^m obtains a maximum (when starting with m=1). |
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+0
9
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| 1, 8, 19, 76, 166, 178, 209, 1907, 20926, 22925, 32653
(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 e^m is greater than the
fractional part of e^k for all k, 1<=k<m.
The next such number must be greater than 100000.
Apparently a duplicate of A091560. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 07 2009]
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FORMULA
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Recursion: a(1):=1, a(k):=min{ m>1 | fract(e^m) > fract(e^a(k-1))}, where fract(x) = x-floor(x).
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EXAMPLE
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a(2)=8, since fract(e^8)= 0.9579870417..., but fract(e^k)<=0.7182818... for 1<=k<=7;
thus fract(e^8)>fract(e^k) for 1<=k<8 and 8 is the minimal exponent > 1 with this property.
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CROSSREFS
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Cf. A153663, A153671, A153679, A153687, A153695, A153707, A154130, A153711, A153719.
Cf. A000149.
Sequence in context: A153026 A057452 A091560 this_sequence A061877 A119284 A153704
Adjacent sequences: A153700 A153701 A153702 this_sequence A153704 A153705 A153706
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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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