A153719 Minimal exponents m such that the fractional part of (Pi-2)^m obtains a maximum (when starting with m=1).

1, 2, 3, 4, 5, 39, 56, 85, 557, 911, 2919, 2921, 4491, 11543, 15724, 98040, 110932, 126659

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 greater than the fractional part of (Pi-2)^k for all k, 1<=k<m.

The next such number must be greater than 200000.

a(19) > 300000. - Robert Price, Mar 26 2019

Links

Table of n, a(n) for n=1..18.

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(6)=39, since fract((Pi-2)^39)= 0.9586616565..., but fract((Pi-2)^k)<=0.9389018... for 1<=k<=38; thus fract((Pi-2)^39)>fract((Pi-2)^k) for 1<=k<39 and 39 is the minimal exponent > 5 with this property.

Mathematica

$MaxExtraPrecision = 100000;
p = 0; Select[Range[1, 10000],
If[FractionalPart[(Pi - 2)^#] > p, p = FractionalPart[(Pi - 2)^#];
True] &] (* Robert Price, Mar 26 2019 *)

Crossrefs

Cf. A153663, A153671, A153679, A153687, A153695, A153707, A153715, A153723, A154130.

Sequence in context: A324276 A324277 A261247 * A024637 A037328 A369782

Adjacent sequences: A153716 A153717 A153718 * A153720 A153721 A153722

Keyword

nonn,more

Author

Hieronymus Fischer, Jan 06 2009

Status

approved