A137994 - OEIS

A137994

a(n) is the smallest integer > a(n-1) such that {Pi^a(n)} < {Pi^a(n-1)}, where {x} = x - floor(x), a(1)=1.

1, 3, 81, 264, 281, 472, 1147, 2081, 3207, 3592, 10479, 12128, 65875, 114791, 118885

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OFFSET

1,2

COMMENTS

The sequence was suggested by Leroy Quet on Pi day 2008, cf. A138324.

The next such number must be greater than 100000. - Hieronymus Fischer, Jan 06 2009

a(16) > 300,000. - Robert Price, Mar 25 2019

LINKS

EXAMPLE

a(3)=81, since {Pi^81}=0.0037011283.., but {Pi^k}>=0.0062766802... for 1<=k<=80; thus {Pi^81}<{Pi^k} for 1<=k<81. - Hieronymus Fischer, Jan 06 2009

MATHEMATICA

$MaxExtraPrecision = 10000;

p = .999;

Select[Range[1, 5000],

If[FractionalPart[Pi^#] < p, p = FractionalPart[Pi^#]; True] &] (* Robert Price, Mar 12 2019 *)

PROG

(PARI) default(realprecision, 10^4); print1(a=1); for(i=1, 100, f=frac(Pi^a); until( frac(Pi^a++)<f, ); print1(", "a))

CROSSREFS

KEYWORD

nonn,more,hard,changed

AUTHOR

EXTENSIONS

a(11)-a(13) from Hieronymus Fischer, Jan 06 2009

Edited by R. J. Mathar, May 21 2010

a(14)-a(15) from Robert Price, Mar 12 2019

STATUS

approved