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A153719 Minimal exponents m such that the fractional part of (Pi-2)^m obtains a maximum (when starting with m=1). 7
1, 2, 3, 4, 5, 39, 56, 85, 557, 911, 2919, 2921, 4491, 11543, 15724, 98040, 110932, 126659 (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 (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 A028427

Adjacent sequences:  A153716 A153717 A153718 * A153720 A153721 A153722

KEYWORD

nonn,more

AUTHOR

Hieronymus Fischer, Jan 06 2009

STATUS

approved

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Last modified October 16 15:22 EDT 2021. Contains 348042 sequences. (Running on oeis4.)