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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. 12
1, 3, 81, 264, 281, 472, 1147, 2081, 3207, 3592, 10479, 12128, 65875, 114791, 118885 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..15.

EXAMPLE

a(3)=81, since fract((Pi^81)=0.0037011283.., but fract(Pi^k)>=0.0062766802... for 1<=k<=80; thus fract(Pi^81)<fract(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

Cf. A001203, A138324, A001672.

Cf. A081464, A153669, A153677, A153685, A153693, A153705, A153713, A154130, A153717 [Hieronymus Fischer, Jan 06 2009]

Sequence in context: A233124 A251694 A274567 * A074386 A116009 A068562

Adjacent sequences:  A137991 A137992 A137993 * A137995 A137996 A137997

KEYWORD

nonn,more

AUTHOR

Leroy Quet and M. F. Hasler, Mar 14 2008

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

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Last modified June 16 14:16 EDT 2021. Contains 345057 sequences. (Running on oeis4.)