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A153701
Minimal exponents m such that the fractional part of e^m obtains a minimum (when starting with m=1).
10
1, 2, 3, 9, 29, 45, 75, 135, 219, 732, 1351, 3315, 4795, 4920, 5469, 28414, 37373
OFFSET
1,2
COMMENTS
Recursive definition: a(1)=1, a(n) = least number m>a(n-1) such that the fractional part of e^m is less than the fractional part of e^k for all k, 1<=k<m.
The next such number must be greater than 100000.
a(18) > 300,000. Robert Price, Mar 23 2019
FORMULA
Recursion: a(1):=1, a(k):=min{ m>1 | fract(e^m) < fract(e^a(k-1))}, where fract(x) = x-floor(x).
EXAMPLE
a(4)=9, since fract(e^9)=0.08392..., but fract(e^k)>=0.08553... for 1<=k<=8; thus fract(e^9)<fract(e^k) for 1<=k<9.
MATHEMATICA
$MaxExtraPrecision = 100000;
p = 1; Select[Range[1, 300000],
If[FractionalPart[E^#] < p, p = FractionalPart[E^#]; True] &] (* Robert Price, Mar 23 2019 *)
KEYWORD
nonn,more
AUTHOR
Hieronymus Fischer, Jan 06 2009
STATUS
approved