A153717 Minimal exponents m such that the fractional part of (Pi-2)^m obtains a minimum (when starting with m=1).

1, 20, 23, 24, 523, 2811, 3465, 3776, 4567, 6145, 8507, 9353, 19790, 41136, 62097, 72506, 107346

Offset

1,2

Comments

Recursive definition: a(1)=1, a(n) = least number m>a(n-1) such that the fractional part of (Pi-2)^m is less than the fractional part of (Pi-2)^k for all k, 1<=k<m.

The next such number must be greater than 200000.

a(18) > 300000. - Robert Price, Mar 26 2019

Links

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

Formula

Recursion: a(1):=1, a(k):=min{ m>1 | fract((Pi-2)^m) < fract((Pi-2)^a(k-1))}, where fract(x) = x-floor(x).

Example

a(3)=23, since fract((Pi-2)^23)=0.0260069.., but fract((Pi-2)^k)>=0.1326... for 1<=k<=22; thus fract((Pi-2)^23)<fract((Pi-2)^k) for 1<=k<23.

Mathematica

$MaxExtraPrecision = 100000;
p = 1; Select[Range[1, 10000],
 If[FractionalPart[(Pi - 2)^#] < p, p = FractionalPart[(Pi - 2)^#];
True] &] (* Robert Price, Mar 26 2019 *)

Crossrefs

Cf. A081464, A153669, A153677, A153685, A153693, A153701, A137994, A153721, A154130.

Sequence in context: A104059 A104057 A268490 * A358424 A303303 A045563

Adjacent sequences: A153714 A153715 A153716 * A153718 A153719 A153720

Keyword

nonn,more

Author

Hieronymus Fischer, Jan 06 2009

Status

approved