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!)
A153669 Minimal exponents m such that the fractional part of (101/100)^m obtains a minimum (when starting with m=1). 14
1, 70, 209, 378, 1653, 2697, 4806, 13744, 66919, 67873, 75666, 81125, 173389, 529938, 1572706, 4751419, 7159431, 7840546, 15896994, 71074288, 119325567 (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 (101/100)^m is less than the fractional part of (101/100)^k for all k, 1<=k<m.

The next term is greater than 2*10^8.

LINKS

Table of n, a(n) for n=1..21.

FORMULA

Recursion: a(1):=1, a(k):=min{ m>1 | fract((101/100)^m) < fract((101/100)^a(k-1))}, where fract(x) = x-floor(x).

EXAMPLE

a(2)=70, since fract((101/100)^70)=0.00676..., but fract((101/100)^k)>=0.01 for 1<=k<=69; thus fract((101/100)^70)<fract((101/100)^k) for 1<=k<70.

MATHEMATICA

p = 1; Select[Range[1, 5000],

If[FractionalPart[(101/100)^#] < p, p = FractionalPart[(101/100)^#];

True] &] (* Robert Price, Mar 21 2019 *)

CROSSREFS

Cf. A081464, A154130, A153673, A153677, A153685, A153693, A153701, A137994, A153717.

Sequence in context: A154361 A165762 A165764 * A235310 A235303 A234564

Adjacent sequences:  A153666 A153667 A153668 * A153670 A153671 A153672

KEYWORD

nonn,more

AUTHOR

Hieronymus Fischer, Jan 06 2009

EXTENSIONS

a(15)-a(21) from Robert Gerbicz, Nov 22 2010

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 19 12:47 EDT 2021. Contains 345129 sequences. (Running on oeis4.)