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A153711 Minimal exponents m such that the fractional part of Pi^m obtains a maximum (when starting with m=1). 8
1, 2, 15, 22, 58, 157, 1030, 5269, 145048, 151710 (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^m is greater than the fractional part of Pi^k for all k, 1<=k<m.

The next such number must be greater than 100000.

a(11) > 300000. - Robert Price, Mar 25 2019

LINKS

Table of n, a(n) for n=1..10.

FORMULA

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

EXAMPLE

a(3)=15, since fract(Pi^15)= 0.9693879984..., but fract(Pi^k)<=0.8696... for 1<=k<=14; thus fract(Pi^15)>fract(Pi^k) for 1<=k<15 and 15 is the minimal exponent > 2 with this property.

MATHEMATICA

$MaxExtraPrecision = 100000;

p = 0; Select[Range[1, 10000],

If[FractionalPart[Pi^#] > p, p = FractionalPart[Pi^#]; True] &] (* Robert Price, Mar 25 2019 *)

CROSSREFS

Cf. A153663, A153671, A153679, A153687, A153695, A153707, A153715, A154130, A153719.

Cf. A001672.

Sequence in context: A169597 A280288 A153712 * A116049 A184236 A023651

Adjacent sequences:  A153708 A153709 A153710 * A153712 A153713 A153714

KEYWORD

nonn,more

AUTHOR

Hieronymus Fischer, Jan 06 2009

EXTENSIONS

a(9)-a(10) from Robert Price, Mar 25 2019

STATUS

approved

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Last modified September 20 17:42 EDT 2021. Contains 347588 sequences. (Running on oeis4.)