login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

LINKS

Table of n, a(n) for n=1..17.

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 *)

CROSSREFS

Cf. A153661, A153669, A153677, A153685, A153693, A153705, A154130, A137994, A153717, A000149.

Sequence in context: A139006 A338868 A213943 * A176678 A277251 A275165

Adjacent sequences:  A153698 A153699 A153700 * A153702 A153703 A153704

KEYWORD

nonn,more

AUTHOR

Hieronymus Fischer, Jan 06 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 15 15:16 EDT 2021. Contains 345049 sequences. (Running on oeis4.)